Intersection cohomology and quantum cohomology of conical symplectic resolutions

TL;DR

This paper proposes a conjecture linking intersection cohomology of singular cones to quantum cohomology of their resolutions, and proves it for hypertoric varieties, enhancing understanding of their algebraic structures.

Contribution

The paper introduces a new conjecture connecting intersection and quantum cohomology for conical symplectic resolutions, and verifies it in the case of hypertoric varieties.

Findings

Confirmed the conjecture for hypertoric varieties

Reconstructed the ring structure on hypertoric intersection cohomology

Established a new link between intersection and quantum cohomology

Abstract

For any conical symplectic resolution, we give a conjecture relating the intersection cohomology of the singular cone to the quantum cohomology of its resolution. We prove this conjecture for hypertoric varieties, recovering the ring structure on hypertoric intersection cohomology that was originally constructed by Braden and the second author.