[Quelques examples de fibrés dans le lieu de base du diviseur thêta généralisé]
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 .
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 .
Accepté le :
Publié le :
@article{CRMATH_2009__347_3-4_173_0,
author = {Casalaina-Martin, Sebastian and Gwena, Tawanda and Teixidor i Bigas, Montserrat},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.12.014/}
}
TY - JOUR AU - Casalaina-Martin, Sebastian AU - Gwena, Tawanda AU - Teixidor i Bigas, Montserrat 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 UR - http://www.numdam.org/articles/10.1016/j.crma.2008.12.014/ DO - 10.1016/j.crma.2008.12.014 LA - en ID - CRMATH_2009__347_3-4_173_0 ER -
%0 Journal Article %A Casalaina-Martin, Sebastian %A Gwena, Tawanda %A Teixidor i Bigas, Montserrat %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 %U http://www.numdam.org/articles/10.1016/j.crma.2008.12.014/ %R 10.1016/j.crma.2008.12.014 %G en %F CRMATH_2009__347_3-4_173_0
Casalaina-Martin, Sebastian; Gwena, Tawanda; Teixidor i Bigas, Montserrat. Some examples of vector bundles in the base locus of the generalized theta divisor. Comptes Rendus. Mathématique, Tome 347 (2009) no. 3-4, pp. 173-176. doi : 10.1016/j.crma.2008.12.014. http://www.numdam.org/articles/10.1016/j.crma.2008.12.014/
[1] 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] The strange duality conjecture for generic curves, J. Amer. Math. Soc., Volume 21 (2008) no. 1, pp. 235-258
[3] 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] 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] Raynaud's vector bundles and base points of the generalized theta divisor, Math. Zeits., Volume 257 (2007) no. 3, pp. 597-611
[6] Raynaud vector bundles | arXiv
[7] The level-rank duality for non-abelian theta functions, Invent. Math., Volume 168 (2007) no. 2, pp. 225-247
[8] 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] Stable maps and Quot schemes, Invent. Math., Volume 152 (2003) no. 3, pp. 625-663
[10] Sections des fibrés vectoriels sur une courbe, Bull. Soc. Math. France, Volume 110 (1982) no. 1, pp. 103-125
[11] On a conjecture of Lange, J. Algebraic Geom., Volume 8 (1999) no. 3, pp. 483-496
Cité par Sources :
