On quantum cohomology of Grassmannians of isotropic lines, unfoldings of Aₙ-singularities, and Lefschetz exceptional collections

Original · EN

The subject of this paper is the big quantum cohomology rings of symplectic isotropic Grassmannians IG(2, 2n). We show that these rings are regular. In particular, by "generic smoothness", we obtain a conceptual proof of generic semisimplicity of the big quantum cohomology for IG(2, 2n). Further, by a general result of Claus Hertling, the regularity of these rings implies that they have a description in terms of isolated hypersurface singularities, which we show in this case to be of type Aₙ₋₁. By the homological mirror symmetry conjecture, these results suggest the existence of a very special full exceptional collection in the derived category of coherent sheaves on IG(2, 2n). Such a collection is constructed in the appendix by Alexander Kuznetsov.