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 KontsevichManin, Getzler etc. on the genus0,1 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.
 Publication:

Physics Letters B
 Pub Date:
 February 1997
 DOI:
 10.1016/S03702693(97)004012
 arXiv:
 arXiv:hepth/9703086
 Bibcode:
 1997PhLB..402...71E
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 latex,13pages. Revised version with a few typos corrected