Stokes Matrices for the Quantum Cohomologies of Grassmannians

TL;DR

This paper proves a conjecture linking the Stokes matrix of quantum cohomology to an exceptional collection in the derived category for Grassmannians, using relations to projective space.

Contribution

It establishes the conjectural relation between Stokes matrices and derived categories for Grassmannians, advancing understanding in quantum cohomology and algebraic geometry.

Findings

Confirmed the conjectural relation for Grassmannians

Connected quantum cohomology of Grassmannians to projective space

Provided a proof based on exceptional collections and derived categories

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 the Grassmannian. The proof is based on the relation between the quantum cohomology of the Grassmannian and that of the projective space.