Intersection cohomology of moduli spaces of vector bundles over curves

Abstract

We compute the intersection cohomology of the moduli spaces $M_{r,d}$ of semistable vector bundles having rank $r$ and degree $d$ over a curve. We do this by relating the Hodge-Deligne polynomial of the intersection cohomology of $M_{r,d}$ to the Donaldson-Thomas invariants of the curve. These invariants can be computed by methods going back to Harder, Narasimhan, Desale and Ramanan. More generally, we introduce Donaldson-Thomas classes in the Grothendieck group of mixed Hodge modules over $M_{r,d}$ and relate them to the class of the intersection complex of $M_{r,d}$. Our methods can be applied to the moduli spaces of semistable objects in arbitrary hereditary categories.

arXiv commentSome comments added. 27 pages

References in corpus (2)

• Cohomological Hall algebra of a symmetric quiver
• Mixed Hodge structures of configuration spaces

Cited by in corpus (3)

• Intersection cohomology of moduli spaces of sheaves on surfaces
• Intersection cohomology of rank two character varieties of surface groups
• Equivariant motivic Hall algebras