A descendent relation in genus 2

Details A descendent relation in genus 2 A descendent relation in genus 2

1998-03-17

arxiv.org/abs/math/9803072v1

Mathematics

Algebraic Geometry

17 pages, LaTeX2e, with (many) PiCTeX figures

Scientific paper

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.

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