A geometric construction of Getzler's relation

Abstract

A geometric construction of Getzler's cohomological relation in the moduli space of 4 pointed elliptic curves is given by a push-forward of a natural rational equivalence in a space of admissible covers. In particular, Getzler's relation is shown to be a rational equivalence. The recursion for the elliptic Gromov-Witten invariants of P^2 predicted by Eguchi, Hori, and Xiong from the Virasoro conjecture is proven via Getzler's equation and the WDVV-equations.

Latex2e 14 pages

References in corpus (1)

• The semi-classical approximation for modular operads

Cited by in corpus (5)

• Geometry of meromorphic functions and intersections on moduli spaces of curves
• Stable maps and Hurwitz schemes in mixed characteristic
• Enumerative geometry of plane curves of low genus
• Descendant invariants and characteristic numbers
• A Change of Coordinates on the Large Phase Space of Quantum Cohomology