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Pandharipande-Pixton have used the geometry of the moduli space of stable quotients to produce relations between tautological Chow classes on the moduli space $M_g$ of smooth genus g curves.
“Conjectural relations in the tautological ring of M ¯ g , n \overline{M}_{g,n} ”
Aaron Pixton · 1918
Earlier work this paper cites.
“Towards an enumerative geometry of the moduli space of curves”
David Mumford · 1983
Earlier work this paper cites.
“Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves”
Enrico Arbarello and Maurizio Cornalba · 1996
Earlier work this paper cites.
“Stacks of stable maps and Gromov-Witten invariants”
Kai Behrend and Yu. Manin · 1996
Earlier work this paper cites.
“Elliptic Gromov-Witten invariants and the generalized mirror conjecture”
Alexander Givental · 1998
Earlier work this paper cites.
“A conjectural description of the tautological ring of the moduli space of curves”
Carel Faber · 1999
Earlier work this paper cites.
“Localization of virtual classes”
Tom Graber and Rahul Pandharipande · 1999
Earlier work this paper cites.
“New moduli spaces of pointed curves and pencils of flat connections” Dedicated to William Fulton on the occasion of his 60th birthday
A. Losev and Y. Manin · 2000
Cited alongside, same era.
“Semisimple Frobenius structures at higher genus”
Alexander˜B. Givental · 2001
Cited alongside, same era.
“Constructions of nontautological classes on moduli spaces of curves”
Tom Graber and Rahul Pandharipande · 2003
Cited alongside, same era.
“Moduli spaces of weighted pointed stable curves”
Brendan Hassett · 2003
Cited alongside, same era.
“Frobenius manifolds, Gromov-Witten theory, and Virasoro constraints”, 2004
Y.˜P. Lee and Rahul Pandharipande · 2004
Cited alongside, same era.
“Relations in the tautological ring of M g M_{g} ”
Eleny-Nicoleta Ionel · 2005
Cited alongside, same era.
“Moduli of weighted stable maps and their gravitational descendants”
Valery Alexeev and G.˜Michael Guy · 2008
Later among the works it cites.
“The Chow ring of M ¯ 0 , m ( ℙ n , d ) \overline{M}_{0,m}(\mathbb{P}^{n},d) ”
Anca˜M. Mustata and Andrei Mustata · 2008
Later among the works it cites.
“Stability conditions, wall-crossing and weighted Gromov-Witten invariants”
Arend Bayer and Yu.˜I. Manin · 2009
Later among the works it cites.
“The moduli space of stable quotients”
Alina Marian, Dragos Oprea and Rahul Pandharipande · 2011
Later among the works it cites.
“Moduli spaces of stable quotients and wall-crossing phenomena”
Yukinobu Toda · 2011
Later among the works it cites.
“Relations on M ¯ g , n \overline{M}_{g,n} via 3 3 -spin structures”
Rahul Pandharipande, Aaron Pixton and Dimitri Zvonkine · 2014
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“The equivariant Gromov-Witten theory of 𝐏 1 {\bf P}^{1} ”
A. Okounkov and R. Pandharipande · 2006
Cited alongside, same era.
“Relations in the tautological ring”
Rahul Pandharipande and Aaron Pixton
Cited in the paper.
“Relations in the tautological ring of the moduli space of curves”
Rahul Pandharipande and Aaron Pixton
Cited in the paper.