We reproduce the quantum cohomology of toric varieties (and of some
hypersurfaces in projective spaces) as the cohomology of certain vertex
algebras with differential. The deformation technique allows us to compute the
cohomology of the chiral de Rham complex over the projective space.Comment: we use the deformation technique from the earlier version of this
note to compute the cohomology of the chiral de Rham complex over the
projective space; the two new results, Theorems 2.5A and B, are explained in
sect. 2.