Algebraic Geometry
Local structure of SUC(3) for a curve of genus 2

Presented by: Michel Raynaud

Serman, Olivier1
1 Laboratoire J.-A. Dieudonné, UMR 6621 du CNRS, Université de Nice, parc Valrose, 06108 Nice cedex 02, France
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).

Received:
Accepted:
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 
@article{CRMATH_2007__344_6_383_0,
     author = {Serman, Olivier},
     title = {Local structure of $ {\mathcal{SU}}_{C}(3)$ for a curve of genus 2},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {383--388},
     publisher = {Elsevier},
     volume = {344},
     number = {6},
     year = {2007},
     doi = {10.1016/j.crma.2007.01.025},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2007.01.025/}
}
TY  - JOUR
AU  - Serman, Olivier
TI  - Local structure of $ {\mathcal{SU}}_{C}(3)$ for a curve of genus 2
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 383
EP  - 388
VL  - 344
IS  - 6
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.crma.2007.01.025/
DO  - 10.1016/j.crma.2007.01.025
LA  - en
ID  - CRMATH_2007__344_6_383_0
ER  - 
%0 Journal Article
%A Serman, Olivier
%T Local structure of $ {\mathcal{SU}}_{C}(3)$ for a curve of genus 2
%J Comptes Rendus. Mathématique
%D 2007
%P 383-388
%V 344
%N 6
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2007.01.025/
%R 10.1016/j.crma.2007.01.025
%G en
%F CRMATH_2007__344_6_383_0
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. https://www.numdam.org/articles/10.1016/j.crma.2007.01.025/

[1] Aslaksen, H.; Drensky, V.; Sadikova, L. Defining relations of invariants of two 3×3 matrices, J. Algebra, Volume 298 (2006), pp. 41-57

[2] Drensky, V. Defining relations for the algebra of invariants of 2×2 matrices, Algebr. Represent. Theory, Volume 6 (2003), pp. 193-214

[3] Formanek, E. Invariants and the ring of generic matrices, J. Algebra, Volume 89 (1984), pp. 178-223

[4] Laszlo, Y. Local structure of the moduli space of vector bundles over curves, Comment. Math. Helv., Volume 71 (1996), pp. 373-401

[5] Le Bruyn, L.; Procesi, C. Semisimple representations of quivers, Trans. Amer. Math. Soc., Volume 317 (1990), pp. 585-598

[6] Ortega, A. On the moduli space of rank 3 vector bundles on a genus 2 curve and the Coble cubic, J. Algebraic Geom., Volume 14 (2005), pp. 327-356

[7] Serman, O. Moduli spaces of orthogonal bundles over an algebraic curve (Preprint, arXiv:) | arXiv

Cited by Sources: