Quantum Cohomology at Higher Genus: Topological Recursion Relations and Virasoro Conditions

Abstract

We construct topological recursion relations (TRR's) at higher genera $g\ge 2$ for general 2-dimensional topological field theories coupled to gravity. These TRR's when combined with Virasoro conditions enable one to determine the number of higher genus holomorphic curves in any Fano varieties. In the case of $C{P}^2$ we reproduce the known results at genus $g=2$.

Latex, 8 pages, the instanton numbers of $C{P}^2$ at genus 3 added, the version to appear in Adv.Theor.Math.Phys

References in corpus (1)

• Enumeration of $n$-fold tangent hyperplanes to a surface