Intersection cohomology of moduli spaces of sheaves on surfaces

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.

25 pages

References in corpus (4)

• Mock Theta Functions
• A computational criterion for the Kac conjecture
• Invariants of moduli spaces of stable sheaves on ruled surfaces
• On rings and categories of general representations

Cited by in corpus (7)

• Vafa-Witten invariants from exceptional collections
• S-duality and refined BPS indices
• Vafa-Witten theory and iterated integrals of modular forms
• Cohomological $\chi$-independence for moduli of one-dimensional sheaves and moduli of Higgs bundles
• Scattering diagrams, stability conditions, and coherent sheaves on ${\mathbb{P}}^2$
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Some moduli spaces of 1-dimensional sheaves on an elliptic ruled surface