The moduli space of rank-3 vector bundles with trivial determinant over a curve of genus 2 and duality

2004/08/23 by Quang Nguyen, Quang Minh Nguyen, Nguyen, Quang Minh
Mathematics · #14E05 #14H60 #14J70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14E05 #msc:14H60 #msc:14J70

paper · pdf · doi:10.48550/arxiv.math/0408318

20 pages. v2

openalex publication_date 2004/08/23 · arxiv created 2004/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let SU_X(3) be the moduli space of semi-stable vector bundles of rank 3 and trivial determinant on a curve X of genus 2. It maps onto P⁸ and the map is a double cover branched over a sextic hypersurface called the Coble sextic. In the dual P⁸ there is a unique cubic hypersurface, the Coble cubic, singular exactly along the abelian surface of degree 1 line bundles on X. We give a new proof that these two hypersurfaces are dual. As an immediate corollary, we derive a Torelli-type result.

Related

• Sur l'espace des modules des fibres vectoriels de rang 3 sur une courbe de genre 2 et la cubique de Coble
• Self-duality of Coble's quartic hypersurface and applications
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• Local structure of SU_C(3) for a curve of genus 2
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