About G-bundles over elliptic curves
Annales de l'Institut Fourier, Volume 48 (1998) no. 2, pp. 413-424.

Let G be a complex algebraic group, simple and simply connected, T a maximal torus and W the Weyl group. One shows that the coarse moduli space M G (X) parametrizing S-equivalence classes of semistable G-bundles over an elliptic curve X is isomorphic to [Γ(T) Z X]/W. By a result of Looijenga, this shows that M G (X) is a weighted projective space.

Soit G un groupe algébrique complexe simple et simplement connexe, T un tore maximal et W le groupe de Weyl. On démontre que l’espace de modules grossier M G paramétrant les classes de S-équivalence de G-fibrés semi-stables sur une courbe elliptique X, est isomorphe à [Γ(T) Z X]/W. D’après un résultat de Looijenga, ceci prouve que M G est un espace projectif anistotrope.

     author = {Laszlo, Yves},
     title = {About $G$-bundles over elliptic curves},
     journal = {Annales de l'Institut Fourier},
     pages = {413--424},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {48},
     number = {2},
     year = {1998},
     doi = {10.5802/aif.1623},
     zbl = {0901.14019},
     mrnumber = {99c:14016},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1623/}
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Laszlo, Yves. About $G$-bundles over elliptic curves. Annales de l'Institut Fourier, Volume 48 (1998) no. 2, pp. 413-424. doi : 10.5802/aif.1623. https://aif.centre-mersenne.org/articles/10.5802/aif.1623/

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