Intersection cohomology of moduli spaces of sheaves on surfaces

TL;DR

This paper explores the intersection cohomology of moduli spaces of semistable sheaves on complex surfaces, linking it to Donaldson-Thomas invariants and providing explicit computations for certain cases.

Contribution

It establishes a relationship between intersection Poincare polynomials and Donaldson-Thomas invariants, with explicit calculations for rank two and three sheaves on ruled surfaces.

Findings

Intersection Poincare polynomials are related to Donaldson-Thomas invariants.

Explicit computations for rank two and three sheaves on ruled surfaces.

Theoretical framework connecting cohomology and invariants.

Abstract

We study intersection cohomology of moduli spaces of semistable vector bundles on a complex algebraic surface. Our main result relates intersection Poincare polynomials of the moduli spaces to Donaldson-Thomas invariants of the surface. In support of this result, we compute explicitly intersection Poincare polynomials for sheaves with rank two and three on ruled surfaces.