
@article{Graber2001,
author = "Graber, Tom and Pandharipande, Rahul",
doi = "10.1307/mmj/1049832895",
fjournal = "The Michigan Mathematical Journal",
journal = "Michigan Math. J.",
month = "04",
number = "1",
pages = "93--110",
publisher = "University of Michigan, Department of Mathematics",
title = "Constructions of nontautological classes of moduli spaces of curves",
url = "http://dx.doi.org/10.1307/mmj/1049832895",
volume = "51",
year = "2003"
}

@article{Keel,
 ISSN = {00029947},
 URL = {http://www.jstor.org/stable/2153922},
 abstract = {We give a new construction of the moduli space via a composition of smooth codimension two blowups and use our construction to determine the Chow ring.},
 author = {Sean Keel},
 journal = {Transactions of the American Mathematical Society},
 number = {2},
 pages = {545-574},
 publisher = {American Mathematical Society},
 title = {Intersection Theory of Moduli Space of Stable N-Pointed Curves of Genus Zero},
 volume = {330},
 year = {1992}
}


@article{petersen2014,
author = "Petersen, Dan",
doi = "10.1215/00127094-2429916",
fjournal = "Duke Mathematical Journal",
journal = "Duke Math. J.",
month = "03",
number = "4",
pages = "777--793",
publisher = "Duke University Press",
title = "The structure of the tautological ring in genus one",
url = "http://dx.doi.org/10.1215/00127094-2429916",
volume = "163",
year = "2014"
}


@article{pikaart1994,
  title={An Orbifold Partition of $\overline{M}^n_g$},
  doi = "10.1007/978-1-4612-4264-2",
  publisher = "Birkhauser Basel",
  author={Pikaart, Martin},
  journal= "The Moduli Space of Curves",
  year={1995}
}

@ARTICLE{faber2013,
   author = {{Faber}, Carel and {Pandharipande}, Rahul},
    title = "{Tautological and non-tautological cohomology of the moduli space of curves}",
  journal = {Handbook of Moduli},
 keywords = {Mathematics - Algebraic Geometry},
     year = 2013,
     publisher = "International Press",
     address = "Boston",
     volume = "Volume I",
     pages = "293--330",
   adsurl = {http://adsabs.harvard.edu/abs/2011arXiv1101.5489F},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{KassPagani1,
	Author = {Kass, Jesse Leo and Pagani, Nicola},
	Date-Added = {2019-11-13 15:07:20 +0000},
	Date-Modified = {2019-11-13 15:07:20 +0000},
	Doi = {10.1090/tran/7724},
	Fjournal = {Transactions of the American Mathematical Society},
	Issn = {0002-9947},
	Journal = {Trans. Amer. Math. Soc.},
	Mrclass = {14H10 (14H40 14K10)},
	Number = {7},
	Pages = {4851--4887},
	Title = {The stability space of compactified universal {J}acobians},
	Url = {https://mathscinet.ams.org/mathscinet-getitem?mr=4009442},
	Volume = {372},
	Year = {2019},
	Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=4009442}}

@article{Pagani2016,
title = "Moduli of abelian covers of elliptic curves ",
journal = "Journal of Pure and Applied Algebra ",
volume = "220",
number = "3",
pages = "1258 - 1279",
year = "2016",
note = "",
issn = "0022-4049",
doi = "http://dx.doi.org/10.1016/j.jpaa.2015.08.020",
url = "http://www.sciencedirect.com/science/article/pii/S0022404915002273",
author = "Nicola Pagani"
}

@article{petersen2016, title={Tautological rings of spaces of pointed genus two curves of compact type}, volume={152}, DOI={10.1112/S0010437X16007478}, number={7}, journal={Compositio Mathematica}, publisher={London Mathematical Society}, author={Petersen, Dan}, year={2016}, pages={1398-1420}}

@Article{Petersen2014b,
author="Petersen, Dan and Tommasi, Orsola", 
title="The Gorenstein conjecture fails for the tautological ring of ${\M_{2,n}}$",
journal="Inventiones mathematicae",
year="2014",
month="Apr",
day="01",
volume="196",
number="1",
pages="139--161",
issn="1432-1297",
doi="10.1007/s00222-013-0466-z",
url="https://doi.org/10.1007/s00222-013-0466-z"
}


@Article{Getzler1998a,
author="Getzler, Ezra",
title="The Semi-Classical Approximation for Modular Operads",
journal="Communications in Mathematical Physics",
year="1998",
volume="194",
number="2",
pages="481--492",
abstract="We study the contribution of one-loop graphs (the semi-classical expansion) problem in the setting of modular operads. As an application, we calculate the Betti numbers of the Deligne-Mumford-Knudsen moduli spaces of stable curves of genus 1 with n marked smooth points.",
issn="1432-0916",
doi="10.1007/s002200050365",
url="http://dx.doi.org/10.1007/s002200050365"
}

@article{Getzler1998,
abstract = {In Part 1 of this paper, we study gravitational descendents of Gromov-Witten invariants for general projective manifolds, applying the Behrend-Fantechi construction of the virtual fundamental classes. In Part 2, we calculate the topological recursion relations in genus 2. There are two of these, one for the second descendent of a field, and one for the first descendents of two fields. The proof uses the results of Part 1 together with a thorough study of intersection theory on the moduli space {\$}\backslashbar{\{}M{\}}{\_}{\{}2,2{\}}{\$}.},
archivePrefix = {arXiv},
arxivId = {math/9801003},
author = {Getzler, Ezra},
eprint = {9801003},
pages = {1--28},
primaryClass = {math},
title = {{Topological recursion relations in genus 2}},
url = {http://arxiv.org/abs/math/9801003},
year = {1998}
}

@InProceedings{Getzlergenus0,
author="Getzler, Ezra",
editor="Dijkgraaf, Robbert H.
and Faber, Carel F.
and van der Geer, Gerard B. M.",
title="Operads and Moduli Spaces of Genus 0 Riemann Surfaces",
booktitle="The Moduli Space of Curves",
year="1995",
publisher="Birkh{\"a}user Boston",
address="Boston, MA",
pages="199--230",
abstract="In this paper, we study two dg (differential graded) operads related to the homology of moduli spaces of pointed algebraic curves of genus 0. These two operads are dual to each other, in the sense of Kontsevich [21] and Ginzburg and Kapranov [14].",
isbn="978-1-4612-4264-2"
}


@article{Faber2005,
author = {Faber, Carel and Pandharipande, Rahul},
file = {:home/jason/Studie/PhD/Papers/2005-007-001-02.pdf:pdf},
volume = {7},
issue = {1},
journal = {JEMS},
pages = {13--49},
title = {{Relative maps and tautological classes}},
year = {2005}
}


@article{Yang2008,
abstract = {This is a note on calculating intersection numbers on moduli spaces of curves. A codimension 3 relation among tautological classes on the moduli space of genus 4 curves is given.},
archivePrefix = {arXiv},
arxivId = {0808.1974},
author = {Yang, Stephanie},
eprint = {0808.1974},
file = {:home/jason/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Yang - 2008 - Calculating intersection numbers on moduli spaces of pointed curves.pdf:pdf},
pages = {10},
title = {{Calculating intersection numbers on moduli spaces of pointed curves}},
url = {http://arxiv.org/abs/0808.1974},
year = {2008}
}


@book{Arbarello2011,
author = {Arbarello, Enrico and Cornalba, Maurizio and Griffiths, Phillip},
isbn = {9783540426882},
title = {Geometry of algebraic curves: Volume II},
year = {2011}
}


@article{Cavalieri2013,
abstract = {We describe double Hurwitz numbers as intersection numbers on the moduli space of curves. Assuming polynomiality of the Double Ramification Cycle (which is known in genera 0 and 1), our formula explains the polynomiality in chambers of double Hurwitz numbers, and the wall crossing phenomenon in terms of a variation of correction terms to the \{$\backslash$psi\} classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle.},
archivePrefix = {arXiv},
arxivId = {1310.4040},
author = {Cavalieri, Renzo and Marcus, Steffen},
doi = {10.4153/CMB-2014-031-6},
eprint = {1310.4040},
file = {:media/jason/DATA/Studie/PhD/Papers/Renzo.pdf:pdf},
issn = {00084395},
title = {{A geometric perspective on the piecewise polynomiality of double Hurwitz numbers}},
url = {http://arxiv.org/abs/1310.4040},
year = {2013}
}

@article{faber2000,
author = "Faber, C. and Pandharipande, R.",
doi = "10.1307/mmj/1030132716",
fjournal = "The Michigan Mathematical Journal",
journal = "Michigan Math. J.",
number = "1",
pages = "215--252",
publisher = "University of Michigan, Department of Mathematics",
title = "Logarithmic series and {Hodge} integrals in the tautological ring. With an appendix by {Don} {Zagier}.",
url = "http://dx.doi.org/10.1307/mmj/1030132716",
volume = "48",
year = "2000"
}


@misc{stacks-project,
  shorthand    = {Stacks},
  author       = {The {Stacks Project Authors}},
  title        = {\textit{Stacks Project}},
  howpublished = {http://stacks.math.columbia.edu}
}




@article{Faber1990II,
 ISSN = {0003486X},
 URL = {http://www.jstor.org/stable/1971526},
 author = {Carel Faber},
 journal = {Annals of Mathematics},
 number = {2},
 pages = {421-449},
 publisher = {Annals of Mathematics},
 title = {Chow Rings of Moduli Spaces of Curves II: Some Results on the Chow Ring of ${\M_4}$},
 volume = {132},
 year = {1990}
}


@article{Faber2012,
abstract = {Let the bielliptic locus be the closure in the moduli space of stable curves of the locus of smooth curves that are double covers of genus 1 curves. In this paper we compute the class of the bielliptic locus in $\backslash$bar\{M\}\_3 in terms of a standard basis of the rational Chow group of codimension-2 classes in the moduli space. Our method is to test the class on the hyperelliptic locus: this gives the desired result up to two free parameters, which are then determined by intersecting the locus with two surfaces in $\backslash$bar\{M\}\_3.},
archivePrefix = {arXiv},
arxivId = {1206.4301},
author = {Faber, Carel and Pagani, Nicola},
eprint = {1206.4301},
file = {:media/jason/DATA/Studie/PhD/Papers/Nicola.pdf:pdf},
title = {{The class of the bielliptic locus in genus 3}},
url = {http://arxiv.org/abs/1206.4301},
year = {2012}
}


@article{Faber1990,
author = {Faber, Carel},
doi = {10.2307/1971525},
file = {:media/jason/DATA/Studie/PhD/Papers/Faber90.pdf:pdf},
isbn = {9780387952185},
issn = {0003486X},
journal = {The Annals of Mathematics},
month = sep,
number = {2},
pages = {331},
pmid = {21453821},
title = {Chow Rings of Moduli Spaces of Curves I: The Chow Ring of ${\M}_3$},
url = {http://www.jstor.org/stable/1971525?origin=crossref},
volume = {132},
year = {1990}
}

@article{Bergstrom2007,
author = {Bergstr\"{o}m, Jonas and Tommasi, Orsola},
year = {2007},
month = {03},
pages = {},
title = {The rational cohomology of ${\M}_4$},
volume = {338},
booktitle = {Mathematische Annalen}
}


@ARTICLE{vanZelm,
   author = {Jason van Zelm},
    title = "{Nontautological Bielliptic Cycles}",
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1612.01206},
 primaryClass = "math.AG",
 keywords = {Mathematics - Algebraic Geometry},
     year = 2016,
    month = dec,
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv161201206V},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}



@book{fulton1984,
  title={Intersection theory},
  author={Fulton, William},
  isbn={9783540121763},
  lccn={83016762},
  series={Ergebnisse der Mathematik und ihrer Grenzgebiete},
  year={1984},
  publisher={Springer-Verlag}
}


@article{Vistoli1989,
author = {Vistoli, Angelo},
doi = {10.1007/BF01388892},
issn = {0020-9910},
journal = {Inventiones mathematicae},
number = {3},
pages = {613--670},
title = {{Intersection theory on algebraic stacks and on their moduli spaces}},
url = {http://www.springerlink.com/index/l8568034m5747385.pdf},
volume = {97},
year = {1989}
}

@article{Deligne1969,
author = {Deligne, Pierre and Mumford, David},
journal = {Publications Math\'{e}matiques de l'IH\'{E}S},
keywords = {algebraic geometry},
language = {eng},
pages = {75-109},
publisher = {Institut des Hautes Études Scientifiques},
title = {The irreducibility of the space of curves of given genus},
url = {http://eudml.org/doc/103899},
volume = {36},
year = {1969},
}


@book{olsson2016,
  title={Algebraic Spaces and Stacks: },
  author={Olsson, Martin},
  isbn={9781470427986},
  lccn={2015043394},
  series={Colloquium Publications},
  url={https://books.google.co.uk/books?id=TvQrDAAAQBAJ},
  year={2016},
  publisher={American Mathematical Society}
}

@book{Behrend,
title={Algebraic Stacks},
author={Kai Behrend and Brian Conrad and Dan Edidin and Barbara Fantechi and William Fulton and Lothar G\"{o}ttsche and Andrew Kresch},
year={Forthcoming}
}


@article{Abramovich2001,
abstract = {The cherry on top of this stacky paper is the following: for any g{\textgreater}1 we give a finite group G such that the moduli space of connected admissible G-covers of genus g is a smooth, fine moduli space, which is a Galois cover of the moduli space of stable curves.   The proof relies on methods introduced by Looijenga and Pikaart-De Jong, and on the theory of twisted G-covers, a theory announced without proofs in math.AG/9811059, section 3, and developed in the first few sections of this paper. This includes a moduli description of the normalization of the Harris-Mumford space of admissible covers, and a study of moduli of stable curves with abelian and non-abelian level structure.},
archivePrefix = {arXiv},
arxivId = {math/0106211},
author = {Abramovich, Dan and Corti, Alessio and Vistoli, Angelo},
doi = {10.1081/AGB-120022434},
eprint = {0106211},
issn = {0092-7872},
pages = {36},
primaryClass = {math},
title = {{Twisted bundles and admissible covers}},
url = {http://arxiv.org/abs/math/0106211},
year = {2001}
}

@article{Harris1982,
author = {Harris, Joe and Mumford, David},
doi = {10.1007/BF01393371},
file = {:home/jason/Studie/PhD/Papers/Kodairadimension.pdf:pdf},
issn = {00209910},
journal = {Inventiones Mathematicae},
number = {1},
pages = {23--86},
title = {{On the Kodaira dimension of the moduli space of curves}},
volume = {67},
year = {1982}
}



@article{castelnuovo1906,
title={Sulle serie algebriche di gruppi di punti appartenenti ad una curva algebrica: nota},
author={Castelnuovo, G.},
year={1906},
pages={337-344},
publisher={Tip. della R. Acc. dei Lincei}
}



@article{Pagani2008,
abstract = {In this work we compute the Chen--Ruan cohomology and the stringy Chow ring of the moduli spaces of smooth and stable {\$}n{\$}-pointed curves of genus 1. We suggest a definition for an Orbifold Tautological Ring in genus 1, which is both a subring of the Chen--Ruan cohomology and of the stringy Chow ring.},
archivePrefix = {arXiv},
arxivId = {0810.2744},
author = {Pagani, Nicola},
doi = {10.5802/aif.2808},
eprint = {0810.2744},
pages = {1--37},
title = {Chen-Ruan cohomology of ${\Mo_{1,n}}$ and ${\M_{1,n}}$},
url = {http://arxiv.org/abs/0810.2744 http://dx.doi.org/10.5802/aif.2808},
year = {2008}
}



@Article{Belorousski1984,
    Author = {Pavel {Belorousski} and Rahul {Pandharipande}},
    Title = {{A descendent relation in genus 2.}},
    FJournal = {{Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV}},
    Journal = {{Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser.}},
    ISSN = {0391-173X},
    Volume = {29},
    Number = {1},
    Pages = {171--191},
    Year = {2000},
    Publisher = {Scuola Normale Superiore, Pisa},
    Language = {English},
    MSC2010 = {81T30 83E30 14H10 14D20 14D22 14N10},
    Zbl = {0981.81063}
}



@article{Tarasca2014,
abstract = {Inside the moduli space of curves of genus 2 with 2 marked points we consider the loci of curves admitting a map to P{\^{}}1 of degree d totally ramified over the two marked points, for d{\textgreater}= 2. Such loci have codimension two. We compute the class of their compactifications in the moduli space of stable curves. Several results will be deduced from this computation.},
archivePrefix = {arXiv},
arxivId = {1401.3057},
author = {Tarasca, Nicola},
eprint = {1401.3057},
file = {:home/jason/Studie/PhD/Papers/DoubleRamifications.pdf:pdf},
keywords = {and phrases,double ramification cycles,hurwitz theory,pseudo-effective cones},
pages = {1--18},
title = {{Double total ramifications for curves of genus 2}},
url = {http://arxiv.org/abs/1401.3057},
volume = {99},
year = {2014}
}



@article{Eisenbud1987,
author = {Eisenbud, David and Harris, Joe},
doi = {10.1007/BF01388710},
file = {:home/jason/.local/share/data/Mendeley Ltd./Mendeley Desktop/Downloaded/Eisenbud, Harris - 1987 - The Kodaira dimension of the moduli space of curves of genus 23.pdf:pdf},
issn = {0020-9910},
journal = {Inventiones Mathematicae},
month = {jun},
number = {2},
pages = {359--387},
title = {{The Kodaira dimension of the moduli space of curves of genus ${\geq 23}$}},
url = {http://link.springer.com/10.1007/BF01388710},
volume = {90},
year = {1987}
}

@Misc{Pixtprogram,
author =   {Aaron Pixton},
title =    {Sage program},
howpublished = {Private circulation, see \textit{http://math.mit.edu/~apixton/research.html}}
}

@Misc{Schmittprogram,
author =   {Johannes Schmitt},
title =    {Sage program},
howpublished = {Private Circulation, Forthcoming Publication}
}


@article{Mochizuki,
  title={The Geometry of the Compactification of the Hurwitz Scheme},
  author={Shinichi Mochizuki},
  journal={Publications of the Research Institute for Mathematical Sciences},
  volume={31},
  number={3},
  pages={355-441},
  year={1995},
  doi={10.2977/prims/1195164048}
}


@article{Cadman,
 ISSN = {00029327, 10806377},
 URL = {http://www.jstor.org/stable/40068067},
 abstract = {We define a Deligne-Mumford stack $X_{D,r} $ which depends on a scheme X, an effective Cartier divisor D ⊂ X, and a positive integer r. Then we show that the Abramovich-Vistoli moduli stack of stable maps into $X_{D,r} $ provides compactifications of the locally closed substacks of $\bar M_{g,n} (x,\beta )$ corresponding to relative stable maps.},
 author = {Charles Cadman},
 journal = {American Journal of Mathematics},
 number = {2},
 pages = {405-427},
 publisher = {Johns Hopkins University Press},
 title = {Using Stacks to Impose Tangency Conditions on Curves},
 volume = {129},
 year = {2007}
}

@article {BertinRomagny,
    AUTHOR = {Bertin, Jos\'e and Romagny, Matthieu},
     TITLE = {Champs de {H}urwitz},
   JOURNAL = {M\'em. Soc. Math. Fr. (N.S.)},
  FJOURNAL = {M\'emoires de la Soci\'et\'e Math\'ematique de France. Nouvelle S\'erie},
    NUMBER = {125-126},
      YEAR = {2011},
     PAGES = {219},
      ISSN = {0249-633X},
      ISBN = {978-2-85629-333-1},
   MRCLASS = {14H30 (11G20 11G30 14H10)},
  MRNUMBER = {2920693},
MRREVIEWER = {Arnaud Beauville},
}

@ARTICLE{hurwitzhodge,
       author = {{Pandharipande}, Rahul and {Tseng}, Hsian-Hua},
        title = "{Higher genus Gromov-Witten theory of the Hilbert scheme of points of the plane and CohFTs associated to local curves}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Algebraic Geometry},
         year = "2017",
        month = "Jul",
          eid = {arXiv:1707.01406},
        pages = {arXiv:1707.01406},
archivePrefix = {arXiv},
       eprint = {1707.01406},
 primaryClass = {math.AG},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2017arXiv170701406P},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{PRvZ,
       author = {{Pagani}, Nicola and {Ricolfi}, Andrea T. and {van Zelm}, Jason},
        title = "{Pullbacks of universal Brill-Noether classes via Abel-Jacobi morphisms}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Algebraic Geometry},
         year = "2018",
        month = "Sep",
          eid = {arXiv:1809.10668},
        pages = {arXiv:1809.10668},
archivePrefix = {arXiv},
       eprint = {1809.10668},
 primaryClass = {math.AG},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2018arXiv180910668P},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@ARTICLE{schmittvanzelm,
       author = {{Schmitt}, Johannes and {van Zelm}, Jason},
        title = "{Intersections of loci of admissible covers with tautological classes}",
      journal = {arXiv e-prints},
     keywords = {Mathematics - Algebraic Geometry},
         year = "2018",
        month = "Aug",
          eid = {arXiv:1808.05817},
        pages = {arXiv:1808.05817},
archivePrefix = {arXiv},
       eprint = {1808.05817},
 primaryClass = {math.AG},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2018arXiv180805817S},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@article{holmesschmitt,
    title={Infinitesimal structure of the pluricanonical double ramification locus},
    author={David Holmes and Johannes Schmitt},
    year={2019},
    eprint={1909.11981},
    archivePrefix={arXiv},
    primaryClass={math.AG}
}

@article {liruan,
	AUTHOR = {Li, An-Min and Ruan, Yongbin},
	TITLE = {Symplectic surgery and {G}romov-{W}itten invariants of
	{C}alabi-{Y}au 3-folds},
	JOURNAL = {Invent. Math.},
	FJOURNAL = {Inventiones Mathematicae},
	VOLUME = {145},
	YEAR = {2001},
	NUMBER = {1},
	PAGES = {151--218},
	ISSN = {0020-9910},
	MRCLASS = {53D45 (14J32 14N35 32Q25 32Q65)},
	MRNUMBER = {1839289},
	MRREVIEWER = {Ignasi Mundet-Riera},
	DOI = {10.1007/s002220100146},
	URL = {https://doi.org/10.1007/s002220100146},
}

@article{Li2002A-degeneration-,
	Author = {Li, Jun},
	Date-Added = {2017-09-09 07:36:59 +0000},
	Date-Modified = {2017-10-02 13:08:08 +0000},
	Journal = {J. Differential Geom.},
	Number = {2},
	Pages = {199--293},
	Publisher = {Lehigh University},
	Title = {A degeneration formula of {GW}-invariants},
	Volume = {60},
	Year = {2002}}
	
@article{Li2001Stable-morphism,
	Author = {Li, Jun},
	Coden = {JDGEAS},
	Date-Added = {2016-10-04 14:52:14 +0000},
	Date-Modified = {2016-10-04 14:52:19 +0000},
	Fjournal = {J. Differential Geom.},
	Issn = {0022-040X},
	Journal = {J. Differential Geom.},
	Mrclass = {14N35},
	Mrnumber = {1882667},
	Mrreviewer = {Andreas Gathmann},
	Number = {3},
	Pages = {509--578},
	Title = {Stable morphisms to singular schemes and relative stable morphisms},
	Url = {http://projecteuclid.org/euclid.jdg/1090348132},
	Volume = {57},
	Year = {2001},
	Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=1882667}}	

@article{Graber2005Relative-virtua,
	Author = {Graber, Tom and Vakil, Ravi},
	Coden = {DUMJAO},
	Date-Added = {2016-10-04 14:54:53 +0000},
	Date-Modified = {2016-10-04 14:54:56 +0000},
	Doi = {10.1215/S0012-7094-05-13011-3},
	Fjournal = {Duke Mathematical Journal},
	Issn = {0012-7094},
	Journal = {Duke Math. J.},
	Mrclass = {14H10 (14C15)},
	Mrnumber = {2176546},
	Mrreviewer = {Ivan S. Kausz},
	Number = {1},
	Pages = {1--37},
	Title = {Relative virtual localization and vanishing of tautological classes on moduli spaces of curves},
	Url = {http://dx.doi.org/10.1215/S0012-7094-05-13011-3},
	Volume = {130},
	Year = {2005},
	Bdsk-Url-1 = {http://www.ams.org/mathscinet-getitem?mr=2176546}}	

@article{Janda2016Double-ramifica,
	Abstract = {Curves of genus g which admit a map to CP1 with specified ramification profile mu over 0 and nu over infinity define a double ramification cycle DR_g(mu,nu) on the moduli space of curves. The study of the restrictions of these cycles to the moduli of nonsingular curves is a classical topic. In 2003, Hain calculated the cycles for curves of compact type. We study here double ramification cycles on the moduli space of Deligne-Mumford stable curves.},
	Author = {Felix Janda and Rahul Pandharipande and Aaron Pixton and Dimitri Zvonkine},
	Date-Added = {2016-10-04 09:41:44 +0000},
	Date-Modified = {2017-08-16 13:05:55 +0000},
	Eprint = {1602.04705},
	Journal = {Publications math{\'e}matiques de l'IH{\'E}S},
	Number = {1},
	Pages = {221--266},
	Title = {Double ramification cycles on the moduli spaces of curves},
	Url = {https://arxiv.org/abs/1602.04705},
	Volume = {125},
	Year = {2017},
	Bdsk-Url-1 = {https://arxiv.org/abs/1602.04705}}	
	
@incollection{Hain2013Normal-function,
	Author = {Richard Hain},
	Booktitle = {Handbook of Moduli, Volume I. Advanced Lectures in Mathematics, Volume XXIV},
	Date-Added = {2013-12-06 09:17:08 +0000},
	Date-Modified = {2013-12-20 15:09:57 +0000},
	Editor = {G. Farkas and I. Morrison},
	Publisher = {International Press, Boston},
	Title = {Normal functions and the geometry of moduli spaces of curves},
	Year = {2013}}	

@article{Grushevsky2012The-zero-sectio,
	Author = {Samuel Grushevsky and Dmitry Zakharov},
	Date-Added = {2013-12-21 16:35:20 +0000},
	Date-Modified = {2014-04-02 12:47:44 +0000},
	Journal = {Duke Math J.},
	Number = {5},
	Pages = {889-1070},
	Title = {The zero section of the universal semiabelian variety, and the double ramification cycle},
	Volume = {163},
	Year = {2014},
	Bdsk-Url-1 = {http://arxiv.org/abs/1206.3534}}	
	
@article {claderjanda,
    AUTHOR = {Clader, Emily and Janda, Felix},
     TITLE = {Pixton's double ramification cycle relations},
   JOURNAL = {Geom. Topol.},
  FJOURNAL = {Geometry \& Topology},
    VOLUME = {22},
      YEAR = {2018},
    NUMBER = {2},
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      ISSN = {1465-3060},
   MRCLASS = {14H10 (14E20 14N35)},
  MRNUMBER = {3748684},
MRREVIEWER = {Eugenii Shustin},
       DOI = {10.2140/gt.2018.22.1069},
       URL = {https://doi.org/10.2140/gt.2018.22.1069},
}	

@article {BCGGM2,
    AUTHOR = {Bainbridge, Matt and Chen, Dawei and Gendron, Quentin and
              Grushevsky, Samuel and M\"{o}ller, Martin},
     TITLE = {Strata of {$k$}-differentials},
   JOURNAL = {Algebr. Geom.},
  FJOURNAL = {Algebraic Geometry},
    VOLUME = {6},
      YEAR = {2019},
    NUMBER = {2},
     PAGES = {196--233},
   MRCLASS = {30F30 (14H15 32J05)},
  MRNUMBER = {3914751},
}

@article {BCGGM1,
    AUTHOR = {Bainbridge, Matt and Chen, Dawei and Gendron, Quentin and
              Grushevsky, Samuel and M\"{o}ller, Martin},
     TITLE = {Compactification of strata of {A}belian differentials},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {167},
      YEAR = {2018},
    NUMBER = {12},
     PAGES = {2347--2416},
      ISSN = {0012-7094},
   MRCLASS = {14H10 (14H15 32G15)},
  MRNUMBER = {3848392},
MRREVIEWER = {Hideki Miyachi},
       DOI = {10.1215/00127094-2018-0012},
       URL = {https://doi.org/10.1215/00127094-2018-0012},
}

@article {HPS,
    AUTHOR = {Holmes, David and Pixton, Aaron and Schmitt, Johannes},
     TITLE = {Multiplicativity of the double ramification cycle},
   JOURNAL = {Doc. Math.},
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    VOLUME = {24},
      YEAR = {2019},
     PAGES = {545--562},
      ISSN = {1431-0635},
   MRCLASS = {14H10 (14C15 30F30)},
  MRNUMBER = {3960120},
}

@article {SchmittDimension,
    AUTHOR = {Schmitt, Johannes},
     TITLE = {Dimension theory of the moduli space of twisted
              {$k$}-differentials},
   JOURNAL = {Doc. Math.},
  FJOURNAL = {Documenta Mathematica},
    VOLUME = {23},
      YEAR = {2018},
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      ISSN = {1431-0635},
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  MRNUMBER = {3861042},
MRREVIEWER = {Hideki Miyachi},
}

@article {FP,
    AUTHOR = {Farkas, Gavril and Pandharipande, Rahul},
     TITLE = {The moduli space of twisted canonical divisors},
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  MRNUMBER = {3789183},
MRREVIEWER = {Alex Massarenti},
       DOI = {10.1017/S1474748016000128},
       URL = {https://doi.org/10.1017/S1474748016000128},
}

@misc{BCGGM3,
    title={The moduli space of multi-scale differentials},
    author={Matt Bainbridge and Dawei Chen and Quentin Gendron and Samuel Grushevsky and Martin Möller},
    year={2019},
    eprint={1910.13492},
    archivePrefix={arXiv},
    primaryClass={math.AG}
}


	
@article{HKP,
	Author = {Holmes, David and Kass, Jesse Leo and Pagani, Nicola},
	Date-Added = {2018-09-14 15:25:51 +0200},
	Date-Modified = {2018-09-14 15:26:00 +0200},
	Doi = {10.1007/s40879-018-0256-7},
	Fjournal = {European Journal of Mathematics},
	Issn = {2199-675X},
	Journal = {Eur. J. Math.},
	Mrclass = {14H40 (14D20 14K30)},
	Number = {3},
	Pages = {1087--1099},
	Title = {Extending the double ramification cycle using {J}acobians},
	Url = {https://doi.org/10.1007/s40879-018-0256-7},
	Volume = {4},
	Year = {2018},
	Bdsk-Url-1 = {https://mathscinet.ams.org/mathscinet-getitem?mr=3851130}}
	
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 volume = {97.1},
 OPTnumber = {},
 OPTseries = {},
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 OPTorganization = {},
 OPTpublisher = {},
 OPTnote = {},
 OPTannote = {},
 OPTurl = {},
 OPTurldate = {},
 OPTlastchecked = {},
 OPTdoi = {},
 OPTisbn = {},
 OPTissn = {},
 OPTlocalfile = {},
 OPTabstract = {},
 OPTkeywords = {},
}	

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@ARTICLE{rossiburyak,
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}

@ARTICLE{pixtonrels,
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}
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}

@article {jandarels,
    AUTHOR = {Janda, Felix},
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@incollection {faberdivisors,
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@Misc{djohnson,
author =   {Drew Johnson},
title =    {mgn - a Sage program for computing products, Faber-Zagier relations, and top intersections on the moduli space of stable curves},
howpublished = {\url{https://pypi.org/project/mgn/}},
year = {2017}
}

@manual{sage,
  Author       = {The {Sage Developers}},
  Title        = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 9.0)},
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@ARTICLE{2019arXiv191202267C,
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 primaryClass = {math.AG},
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}

@ARTICLE{2019arXiv190312526G,
       author = {{Grosse}, Harald and {Hock}, Alexander and {Wulkenhaar}, Raimar},
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 primaryClass = {math-ph},
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@ARTICLE{somerstep,
  title={Boundary Expression for {Chern} Classes of the Hodge Bundle on Spaces of Cyclic Covers},
  author={Bryson Owens and Seamus Somerstep},
  journal = {arXiv e-prints},
  year={2019}
}
