Quantum cohomology and Virasoro algebra

We propose that the Virasoro algebra controls quantum cohomologies of general Fano manifolds M(c1(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 ect. 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 χ(M), the Euler characteristic of the manifold M.