Quantum Cohomology and Virasoro Algebra

Abstract

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 $M$.

latex,13pages. Revised version with a few typos corrected

References in corpus (1)

• A mirror theorem for toric complete intersections

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