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

2000/12/29 by Richard Earl, Frances Kirwan, Earl, Richard +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #advanced mathematical theories #math.AG

paper · pdf · doi:10.48550/arxiv.math/0012260

18 pages, to appear in Quart. J. Math

arxiv created 2000/12/29 · openalex publication_date 2000/12/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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