Comptes Rendus
Algebraic Geometry
Some examples of vector bundles in the base locus of the generalized theta divisor
Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 173-176.

We show that, on the moduli space of semi-stable vector bundles of fixed rank and determinant (of any degree) on a curve, the base locus of the theta divisor as well as its n-multiples is large. This extends known results for the case of trivial determinant and n=1.

On prouve que, sur l'espace de modules des fibrés stables de déterminant fixé (et degré quelconque) sur une courbe, le lieu de base du diviseur thêta généralisé ainsi que ses n-multiples est assez grand. Ce travail étend des résultats connus pour le cas de degré zéro et n=1.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.12.014

Sebastian Casalaina-Martin 1; Tawanda Gwena 2; Montserrat Teixidor i Bigas 2

1 Department of Mathematics, University of Colorado at Boulder, Campus Box 395, Boulder, CO 80309-0395, USA
2 Mathematics Department, Tufts University, Medford MA 02155, USA
@article{CRMATH_2009__347_3-4_173_0,
     author = {Sebastian Casalaina-Martin and Tawanda Gwena and Montserrat Teixidor i Bigas},
     title = {Some examples of vector bundles in the base locus of the generalized theta divisor},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {173--176},
     publisher = {Elsevier},
     volume = {347},
     number = {3-4},
     year = {2009},
     doi = {10.1016/j.crma.2008.12.014},
     language = {en},
}
TY  - JOUR
AU  - Sebastian Casalaina-Martin
AU  - Tawanda Gwena
AU  - Montserrat Teixidor i Bigas
TI  - Some examples of vector bundles in the base locus of the generalized theta divisor
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 173
EP  - 176
VL  - 347
IS  - 3-4
PB  - Elsevier
DO  - 10.1016/j.crma.2008.12.014
LA  - en
ID  - CRMATH_2009__347_3-4_173_0
ER  - 
%0 Journal Article
%A Sebastian Casalaina-Martin
%A Tawanda Gwena
%A Montserrat Teixidor i Bigas
%T Some examples of vector bundles in the base locus of the generalized theta divisor
%J Comptes Rendus. Mathématique
%D 2009
%P 173-176
%V 347
%N 3-4
%I Elsevier
%R 10.1016/j.crma.2008.12.014
%G en
%F CRMATH_2009__347_3-4_173_0
Sebastian Casalaina-Martin; Tawanda Gwena; Montserrat Teixidor i Bigas. Some examples of vector bundles in the base locus of the generalized theta divisor. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 173-176. doi : 10.1016/j.crma.2008.12.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.014/

[1] D. Arcara A lower bound for the dimension of the base locus of the generalized theta divisor, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 340 (2005) no. 2, pp. 131-134

[2] P. Belkale The strange duality conjecture for generic curves, J. Amer. Math. Soc., Volume 21 (2008) no. 1, pp. 235-258

[3] J.M. Drezet; M.S. Narasimhan Groupe de Picard des variétés de modules de fibres semi-stables sur les courbes algebriques, Invent. Math., Volume 97 (1989) no. 1, pp. 53-94

[4] T. Gwena; M. Teixidor i Bigas Maps between moduli spaces of vector bundles and the base locus of the theta divisor, Amer. Math. Soc., Volume 137 (2009), pp. 853-861

[5] G. Hein Raynaud's vector bundles and base points of the generalized theta divisor, Math. Zeits., Volume 257 (2007) no. 3, pp. 597-611

[6] G. Hein Raynaud vector bundles | arXiv

[7] A. Marian; D. Oprea The level-rank duality for non-abelian theta functions, Invent. Math., Volume 168 (2007) no. 2, pp. 225-247

[8] M. Popa On the base locus of the generalized theta divisor, C. R. Acad. Sci. Paris, Ser. I, Volume 329 (1999) no. 6, pp. 507-512

[9] M. Popa; M. Roth Stable maps and Quot schemes, Invent. Math., Volume 152 (2003) no. 3, pp. 625-663

[10] M. Raynaud Sections des fibrés vectoriels sur une courbe, Bull. Soc. Math. France, Volume 110 (1982) no. 1, pp. 103-125

[11] B. Russo; M. Teixidor i Bigas On a conjecture of Lange, J. Algebraic Geom., Volume 8 (1999) no. 3, pp. 483-496

Cited by Sources:

Comments - Policy