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# Systèmes linéaires sur le champ algébrique des fibrés quasi-paraboliques sur une courbe

Abstract : This thesis is a study of linear systems on the algebraic stack of quasi-parabolic bundles on an algebraic curve. In the first part we prove that the $\ell$th tensor power of the determinant line bundle on the moduli space of semistable parabolic bundles is a linear system without base points, as soon as $\ell$ is greater than or equal to an integer $\ell_0$, which just depends on the rank of the underlying vector bundles. This fact results from the existence of a quasi-parabolic analog of Grothendieck's scheme of quotients. In the second part we study the more general case of linear systems on the algebraic stack of quasi-parabolic bundles. The theorem on the parabolic determinant line bundle of the first part allows to identify the base locus of a linear system and the closed substack of quasi-parabolic bundles that are unstable with respect to the parabolic weights, determined by the linear system.
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https://tel.archives-ouvertes.fr/tel-00002544
Contributor : Francesca Gavioli <>
Submitted on : Wednesday, March 12, 2003 - 2:16:22 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:06:38 PM

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• HAL Id : tel-00002544, version 1

### Citation

Francesca Gavioli. Systèmes linéaires sur le champ algébrique des fibrés quasi-paraboliques sur une courbe. Mathématiques [math]. Université de Nantes, 2003. Français. ⟨tel-00002544⟩

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