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The line bundles on the moduli of parabolic G-bundles over curves and their sections

Identifieur interne : 002518 ( Istex/Curation ); précédent : 002517; suivant : 002519

The line bundles on the moduli of parabolic G-bundles over curves and their sections

Auteurs : Yves Laszlo [France] ; Christoph Sorger [France]

Source :

RBID : ISTEX:B3CF9F845D06279C40D7D9E46843832A9F73C6AC

English descriptors

Abstract

Abstract: 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.

Url:
DOI: 10.1016/S0012-9593(97)89929-6

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ISTEX:B3CF9F845D06279C40D7D9E46843832A9F73C6AC

Le document en format XML

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<front>
<div type="abstract" xml:lang="en">Abstract: 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.</div>
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