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On the Cohomology of Moduli of Vector Bundles

Ajneet Dhillon
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Abstract

We compute some Hodge and Betti numbers of the moduli space of stable rank $r$ degree $d$ vector bundles on a smooth projective curve. We do not assume $r$ and $d$ are coprime. In the process we equip the cohomology of an arbitrary algebraic stack with a functorial mixed Hodge structure. This Hodge structure is computed in the case of the moduli stack of rank $r$, degree $d$ vector bundles on a curve. Our methods also yield a formula for the Poincare polynomial of the moduli stack that is valid over any ground field.

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Ajneet Dhillon. 2003-10-21. On the Cohomology of Moduli of Vector Bundles. https://arxiv.org/abs/math/0310299

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