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A descendent relation in genus 2. (English) Zbl 0981.81063

Summary: 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.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E30 String and superstring theories in gravitational theory
14H10 Families, moduli of curves (algebraic)
14D20 Algebraic moduli problems, moduli of vector bundles
14D22 Fine and coarse moduli spaces
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
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