Revisiting the moduli space of semistable G-bundles over elliptic curves
[Les espaces des modules des G-fibrés semistables sur une courbe elliptique revisités]
Annales de l'Institut Fourier, Online first, 27 p.

Nous démontrons que l’espace de module des G-fibrés semistables sur une courbe elliptique pour un groupe réductif G est isomorphe à une certaine puissance de la courbe elliptique quotientée par un groupe de Weyl qui dépendent du type topologique des fibrés considérés. Ceci généralise un résultat de Laszlo à toute composante connexe de l’espace des modules et permet de retrouver ainsi la description globale de l’espace des modules due initialement à Schweigert et Friedman–Morgan–Witten. Les démonstrations n’utilisent que de la géométrie algébrique et sont aussi valables en caractéristique positive.

We show that the moduli space of semistable G-bundles on an elliptic curve for a reductive group G is isomorphic to a power of the elliptic curve modulo a certain Weyl group which depend on the topological type of the bundle. This generalises a result of Laszlo to arbitrary connected components and recovers the global description of the moduli space due to Friedman–Morgan–Witten and Schweigert. The proof is entirely in the realm of algebraic geometry and works in arbitrary characteristic.

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DOI : https://doi.org/10.5802/aif.3405
Classification : 14D20,  14D23
Mots clés : espace des modules, G-fibrés principaux, espaces principaux, courbe elliptique, semistable
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     author = {Fr\u{a}\c{t}il\u{a}, Drago\c{s}},
     title = {Revisiting the moduli space of semistable $G$-bundles over elliptic curves},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     year = {2021},
     doi = {10.5802/aif.3405},
     language = {en},
     note = {Online first},
}
Frăţilă, Dragoş. Revisiting the moduli space of semistable $G$-bundles over elliptic curves. Annales de l'Institut Fourier, Online first, 27 p.

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