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A geometric construction of Getzler's relation

Rahul Pandharipande
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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.

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BibTeXRIS

Rahul Pandharipande. 1997-05-17. A geometric construction of Getzler's relation. https://arxiv.org/abs/alg-geom/9705016

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