Self-duality of Coble's quartic hypersurface and applications

2001/09/27 by Christian Pauly, Pauly, Christian
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG

paper · pdf · doi:10.48550/arxiv.math/0109218

arxiv created 2001/09/27 · openalex publication_date 2001/09/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The moduli space M₀ of semi-stable rank 2 vector bundles with fixed trivial determinant over a non-hyperelliptic curve C of genus 3 is isomorphic to a quartic hypersurface in P⁷ (Coble's quartic). We show that M₀ is self-dual and that its polar map associates to a stable bundle E ∈ M₀ a bundle F which is characterized by dim H⁰(C, E ⊗ F) = 4. The projective space PH⁰(C, E ⊗ F) is equipped with a net of quadrics Πand it is shown that the map which associates to E ∈ M₀ the isomorphism class of the plane quartic Hessian curve of Πis a dominant map to the moduli space of genus 3 curves.

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• Sur l'espace des modules des fibres vectoriels de rang 3 sur une courbe de genre 2 et la cubique de Coble
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• The Frobenius map, rank 2 vector bundles and Kummer's quartic surface in characteristic 2 and 3
• The tangent space to the moduli space of vector bundles on a curve and the singular locus of the theta divisor of the jacobian