%0 Journal Article
%T Quantum Cohomology and Virasoro Algebra
%A Tohru Eguchi
%A Kentaro Hori
%A Chuan-Sheng Xiong
%J Mathematics
%D 1997
%I arXiv
%R 10.1016/S0370-2693(97)00401-2
%X We propose that the Virasoro algebra controls quantum cohomologies of general Fano manifolds $M$ ($c_1(M)>0$) and determines their partition functions at all genera. We construct Virasoro operators in the case of complex projective spaces and show that they reproduce the results of Kontsevich-Manin, Getzler etc. on the genus-0,1 instanton numbers. We also construct Virasoro operators for a wider class of Fano varieties. The central charge of the algebra is equal to $\chi(M)$, the Euler characteristic of the manifold $M$.
%U http://arxiv.org/abs/hep-th/9703086v2