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

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

1998-01-05

arxiv.org/abs/hep-th/9801010v2

Adv.Theor.Math.Phys.2:219-229,1998

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

We construct topological recursion relations (TRR's) at higher genera $g\ge2$
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 $CP^2$
we reproduce the known results at genus $g=2$.

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