A descendent relation in genus 2

Abstract

A new codimension 2 relation among descendent strata in the moduli space of stable, 3-pointed, genus 2 curves is found. The space of pointed admissible double covers is used in the calculation. The resulting differential equations satisfied by the genus 2 gravitational potentials of varieties in Gromov-Witten theory are described. These are analogous to the WDVV-equations in genus 0 and Getzler's equations in genus 1. As an application, genus 2 descendent invariants of the projective plane are determined, including the classical genus 2 Severi degrees.

17 pages, LaTeX2e, with (many) PiCTeX figures

References in corpus (7)

• Higher genus symplectic invariants and sigma model coupled with gravity
• Quantum Cohomology and Virasoro Algebra
• Topological recursion relations in genus 2
• Relations between the correlators of the topological sigma-model coupled to gravity
• Quantum Cohomology of a Product
• Localization of virtual classes
• Counting plane curves of any genus

Cited by in corpus (21)

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Semisimple Frobenius structures at higher genus
• BCOV theory via Givental group action on cohomological field theories
• Relations in the tautological ring of the moduli space of curves
• A Genus-3 Topological Recursion Relation
• Open topological strings and integrable hierarchies: Remodeling the A-model
• Geometry of meromorphic functions and intersections on moduli spaces of curves
• Moduli Spaces of Higher Spin Curves and Integrable Hierarchies
• Witten's conjecture, Virasoro conjecture, and invariance of tautological equations
• Ramanujan Identities and Quasi-Modularity in Gromov-Witten Theory
• Tautological relations in Hodge field theory
• Tautological relations via r-spin structures
• Belorousski-Pandharipande relation in dGBV algebras
• Topological recursion relations from Pixton's formula
• Topological gravity in genus 2 with two primary fields
• Incidence varieties in the projectivized $k$-th Hodge bundle over curves with rational tails
• Tevelev degrees and Hurwitz moduli spaces
• $N=1$ formal genus $0$ Gromov-Witten theories and Givental's formalism
• The fourth tautological group of $\overline{{\mathcal{M}}_{g,n}}$ and relations with the cohomology
• Relative maps and tautological classes
• Virasoro Constraints For Quantum Cohomology