What question did this study set out to answer?

The aim is to compute the intersection cohomology of moduli spaces of semistable vector bundles over curves.

May 10, 2026Open Access

Intersection cohomology of moduli spaces of vector bundles over curves

Puntos clave

The aim is to compute the intersection cohomology of moduli spaces of semistable vector bundles over curves.
Computed intersection cohomology of moduli spaces ${M}_{r,d}$ of semistable vector bundles.
Related the Hodge–Deligne polynomial of the intersection cohomology to Donaldson–Thomas invariants.
Introduced Donaldson–Thomas classes in the Grothendieck group of mixed Hodge modules.
Established a relation between Hodge–Deligne polynomial and Donaldson–Thomas invariants.
Introduced new classes in the context of intersection complex over ${M}_{r,d}$.

Resumen

Abstract We compute the intersection cohomology of the moduli spaces Mₑ, ₃ 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 Mₑ, ₃ 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 Mₑ, ₃, and relate them to the class of the intersection complex of Mₑ, ₃. Our methods can be applied to the moduli spaces of semistable objects in arbitrary hereditary categories.

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