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

Tohru Eguchi; Chuan-Sheng Xiong

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

High Energy Physics - Theory 2008-11-26 v2 Algebraic Geometry

Authors: Tohru Eguchi , Chuan-Sheng Xiong

Abstract

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 $g=2$ .

Keywords

quantum cohomology higher genus topological recursion relations Virasoro conditions topological field theory Fano varieties holomorphic curves

Cite

@article{arxiv.hep-th/9801010,
  title  = {Quantum Cohomology at Higher Genus: Topological Recursion Relations and Virasoro Conditions},
  author = {Tohru Eguchi and Chuan-Sheng Xiong},
  journal= {arXiv preprint arXiv:hep-th/9801010},
  year   = {2008}
}

Comments

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

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

Abstract

Keywords

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