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• W2030221275 abstract "Soient X une courbe complexe, lisse, projective et connexe et G un groupe algébrique complexe, simple et simplement connexe. Nous calculons le groupe de Picard du champ des G-fibrés quasi-paraboliques sur X, décrivons explicitement ses générateurs pour G de type classique ou G2, puis identifions les espaces de sections globales correspondants avec les espaces de vacua de Tsuchiya, Ueno et Yamada. La méthode utilise le théorème d'uniformisation qui décrit ces champs comme doubles quotients de certains groupes algébriques de dimension infinie. Nous décrivons le fibré dualisant du champ des G-fibrés et montrons qu'il admet une unique racine carrée, que nous construisons explicitement. Si G n'est pas simplement connexe, la racine carrée dépend du choix d'une thêta-caractéristique. Ces résultats sur les champs permettent de retrouver le théorème de Drezet et Narasimhan (pour l'espace de modules grossier) et de montrer un énoncé analogue dans le cas G = Sp2r. Nous montrons aussi que le module grossier des SOr-fibrés n'est pas localement factoriel pour r ≥ 7. Let X be a complex, smooth, complete and connected curve and G be a complex simple and simply connected algebraic group. We compute the Picard group of the stack of quasi-parabolic G-bundles over X, describe explicitly its generators for classical G and G2 and then identify the corresponding spaces of global sections with the vacua spaces of Tsuchiya, Ueno and Yamada. The method uses the uniformization theorem which describes these stacks as double quotients of certain infinite dimensional algebraic groups. We describe also the dualizing bundle of the stack of G-bundles and show that it admits a unique square root, which we construct explicitly. If G is not simply connected, the square root depends on the choice of a theta-characteristic. These results about stacks allow to recover the Drezet-Narasimhan theorem (for the coarse moduli space) and to show an analogous statement when G = Sp2r. We prove also that the coarse moduli spaces of semi-stable SOr-bundles are not locally factorial for r ≥ 7." @default.
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• W2030221275 date "1997-01-01" @default.
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• W2030221275 title "The line bundles on the moduli of parabolic G-bundles over curves and their sections" @default.
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• W2030221275 doi "https://doi.org/10.1016/s0012-9593(97)89929-6" @default.
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