The Hodge Numbers of the Moduli Spaces of Vector Bundles over a Riemann surface

Details The Hodge Numbers of the Moduli Spaces of Vector Bundles over a Riemann surface The Hodge Numbers of the Moduli Spaces of Vector Bundles over a Riemann surface

2000-12-29

arxiv.org/abs/math/0012260v1

Mathematics

Algebraic Geometry

18 pages, to appear in Quart. J. Math

Scientific paper

Inductive formulas for the Betti numbers of the moduli spaces of stable holomorphic vector bundles of coprime rank and degree over a fixed Riemann surface of genus at least two were obtained by Harder, Narasimhan, Desale and Ramanan using number theoretic methods and the Weil conjectures and were rederived by Atiyah and Bott using gauge theory. In this note we observe that there are similar inductive formulas for determining the Hodge numbers of these moduli spaces.

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