Intersection cohomology of moduli spaces of vector bundles over curves

We compute the intersection cohomology of the moduli spaces Mr,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 Mr,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 Mr,d , and relate them to the class of the intersection complex of Mr,d . Our methods can be applied to the moduli spaces of semistable objects in arbitrary hereditary categories.