Algebraic Geometry
Local structure of SUC(3) for a curve of genus 2
Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 383-388.

The aim of this Note is to give a precise description of the local structure of the moduli space SUC(3) of rank 3 vector bundles on a curve C of genus 2, which is in particular shown to be a local complete intersection. This allows us to investigate the local structure of the branch locus of the theta map, the dual of which is known to be the Coble cubic in PH0(JC1,3Θ).

Le but de cette Note est de donner une description précise de la structure locale en tout point de l'espace de modules SUC(3) des fibrés vectoriels de rang 3 sur une courbe de genre 2. Cette étude montre notamment que cet espace est localement intersection complète. Elle permet aussi d'analyser la structure locale du lieu de branchement de l'application thêta, qui n'est autre que la variété duale de la cubique de Coble dans PH0(JC1,3Θ).

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Published online:
DOI: 10.1016/j.crma.2007.01.025
Serman, Olivier 1

1 Laboratoire J.-A. Dieudonné, UMR 6621 du CNRS, Université de Nice, parc Valrose, 06108 Nice cedex 02, France
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Serman, Olivier. Local structure of $ {\mathcal{SU}}_{C}(3)$ for a curve of genus 2. Comptes Rendus. Mathématique, Volume 344 (2007) no. 6, pp. 383-388. doi : 10.1016/j.crma.2007.01.025. http://www.numdam.org/articles/10.1016/j.crma.2007.01.025/

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