Intersection cohomology of moduli spaces of sheaves on surfaces

Abstract

We study intersection cohomology of moduli spaces of semist able vector bundles on a complex algebraic surface. Our main result relates inte rsection Poincar ́e polynomials of the moduli spaces to Donaldson-Thomas invariants of the sur face. In support of this result, we compute explicitly intersection Poincar ́e polynomials fo r sheaves with rank two and three on ruled surfaces.