Sur l'espace des modules des fibres vectoriels de rang 3 sur une courbe de genre 2 et la cubique de Coble

2003/09/01 by Angela Ortega Ortega, Ortega, Angela Ortega
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0309019

thesis, 68 pages with 2 figures

arxiv created 2003/12/09 · arxiv updated 2009/12/01

Abstract

In this thesis we have proved a conjecture about the moduli space SU_X(3) of semi-stable rank 3 vector bundles with trivial determinant on a genus 2 curve X, due to I. Dolgachev. Given X a smooth projective curve of genus 2, and the embedding of the jacobian JX into |3Θ|, A. Coble proved, at the begining of XX century, that there exists a unique cubic hypersurface C in |3Θ|* ≃ P⁸, JX[3]-invariant and singular along JX. On the other hand, we have a map of degree 2 from SU_X(3) over |3Θ|, ramified along a sextic hypersurface B. The Dolgachev's conjecture affirms that the sextic B is the dual variety of the Coble's cubic C.

Related

• The moduli space of rank-3 vector bundles with trivial determinant over a curve of genus 2 and duality
• Local structure of SU_C(3) for a curve of genus 2
• Self-duality of Coble's quartic hypersurface and applications
• Hecke cycles on moduli of vector bundles and orbital degeneracy loci
• Vector bundles on the cubic threefold