A Torelli theorem for moduli spaces of principal bundles over a curve

[Un théorème de Torelli pour les espaces des modules de fibrés principaux sur une courbe]

Biswas, Indranil ; Hoffmann, Norbert

Annales de l'Institut Fourier, Tome 62 (2012), p. 87-106 / Harvested from Numdam

Résumé

Soient $\displaystyle X$ et $\displaystyle X^{\prime}$ des surfaces de Riemann compactes de genre au moins 3, et $\displaystyle G$ et $\displaystyle G^{\prime}$ des groupes complexes réductifs non abéliens. Si une composante $\displaystyle \mathcal{M}_G^d(X)$ de l’espace des modules de $G$–fibrés principaux semi-stables sur $X$ est isomorphe à une composante $\displaystyle \mathcal{M}_{G^{\prime}}^{d^{\prime}}(X^{\prime})$, alors $X$ est isomorphe à $X^{\prime}$.

Abstract

Let $X$ and $X^{\prime}$ be compact Riemann surfaces of genus $\ge 3$, and let $G$ and $G^{\prime}$ be nonabelian reductive complex groups. If one component $\mathcal{M}_G^d( X)$ of the coarse moduli space for semistable principal $G$–bundles over $X$ is isomorphic to another component $\mathcal{M}_{G^{\prime}}^{d^{\prime}}(X^{\prime})$, then $X$ is isomorphic to $X^{\prime}$.

Détail

Publié le : 2012-01-01

MR 2986266 | Zbl 1268.14010 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.2700
Classification:  14D20,  14C34
Mots clés: Fibré principal, espace des modules, théorème de Torelli

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