On vector bundles on curves over $ {\overline{\mathbb{F}}}_{p}$

Indranil Biswas; A.J. Parameswaran

doi:10.1016/j.crma.2012.01.006

Algebraic Geometry

On vector bundles on curves over

{\bar{F}}_{p}

Presented by: Claire Voisin

Indranil Biswas ¹; A.J. Parameswaran ¹

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 213-216.

Abstract
Résumé

Let V be a vector bundle over an irreducible smooth projective curve defined over the field ${\bar{F}}_{p}$ . For any integer $r \in (0, rank (V))$ , let ${Gr}_{r} (V)$ be the Grassmann bundle parametrizing r-dimensional quotients of the fibers of V. Let L be a line bundle over ${Gr}_{r} (V)$ such that $L \cdot C > 0$ for every irreducible closed curve $C \subset {Gr}_{r} (V)$ . We prove that L is ample.

Soit V un fibré vectoriel sur une courbe projective lisse irréductible définie sur ${\bar{F}}_{p}$ . Pour tout entier $r \in (0, rank (V))$ , soit ${Gr}_{r} (V)$ le fibré en grassmanniennes paramétrisant les quotients de dimension r des fibrés de V. Soit L un fibré en droites sur ${Gr}_{r} (V)$ tel que $L \cdot C > 0$ pour toute courbe fermée irréducible $C \subset {Gr}_{r} (V)$ . On prouve alors que L est ample.

Received: 2011-11-14
Accepted: 2012-01-11
Published online: 2012-01-19

DOI: 10.1016/j.crma.2012.01.006

Author's affiliations:

Indranil Biswas ¹; A.J. Parameswaran ¹

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

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     title = {On vector bundles on curves over $ {\overline{\mathbb{F}}}_{p}$},
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Indranil Biswas; A.J. Parameswaran. On vector bundles on curves over $ {\overline{\mathbb{F}}}_{p}$. Comptes Rendus. Mathématique, Volume 350 (2012) no. 3-4, pp. 213-216. doi : 10.1016/j.crma.2012.01.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.006/

References
Cited by

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