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.

arXiv comment25 pages, 5 figures

References in corpus (6)

• Quantum Cohomology Rings of Toric Manifolds
• Geometry and analytic theory of Frobenius manifolds
• Elliptic Gromov - Witten invariants and the generalized mirror conjecture
• Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces
• Gromov-Witten invariants of blow-ups
• Stokes Matrices for the Quantum Cohomologies of Grassmannians

Cited by in corpus (5)

• An integral structure in quantum cohomology and mirror symmetry for toric orbifolds
• An analogue of Dubrovin's conjecture
• Local Gromov-Witten invariants of cubic surfaces via nef toric degeneration
• The Stokes Phenomenon and Some Applications
• Invariants of hypergeometric groups for Calabi-Yau complete intersections in weighted projective spaces