THE MODULI SPACE OF CURVES AND GROMOV-WITTEN THEORY

By Ravi Vakil. 2006

76 citations recorded by the source corpus.

The goal of this article is to motivate and describe how Gromov-Witten the- ory can and has provided tools to understand the moduli space of curves. For example, ideas and methods from Gromov-Witten theory have led to both conjectures and theorems showing that the tautological part of the cohomology ring has a remarkable and profound structure. As an illustration, we describe a new approach to Faber's intersection number conjecture via branched covers of the projective line (work with I.P. Goulden and D.M. Jackson, based on work with T. Graber). En route we review the work of a large number of mathematicians.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3091b7a7e9ddb9304138abc65080dd6805483f7b

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In Discrete Mathematics and Combinatorics

1. Sergey Shadrin
2. L. Spitz
3. Dimitri Zvonkine

In Geometry and Topology

1. Dimitri Zvonkine
2. L. Spitz
3. Sergey Shadrin

Citations in the corpus

• Equivalence of ELSV and Bouchard–Mariño conjectures for $$r$$r-spin Hurwitz numbers (2013, background): “, ψn ∈ H(2)(Mg,n,Q) that one usually defines on Mg,n (see, for instance, [36], Section 3.”