Quantum Cohomology at Higher Genus: Topological Recursion Relations and   Virasoro Conditions
  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 $g=2$. 
Tohru Eguchi and Chuan-Sheng Xiong