Stokes Matrix for the Quantum Cohomology of Cubic Surfaces

Abstract

We prove the conjectural relation between the Stokes matrix for the quantum cohomology and an exceptional collection generating the derived category of coherent sheaves in the case of smooth cubic surfaces. The proof is based on a toric degeneration of cubic surfaces, the Givental's mirror theorem for toric manifolds, and the Picard-Lefschetz theory.