A geometric construction of Getzler's relation
Rahul Pandharipande
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 P2 predicted by Eguchi, Hori, and Xiong from the Virasoro conjecture is proven via Getzler's equation and the WDVV-equations.
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