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

• [1] School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
• [2] Freie Universität Berlin, Institut fûr Mathematik, Arnimallee 3, 14195 Berlin, Germany
• Volume: 62, Issue: 1, page 87-106
• ISSN: 0373-0956

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## Abstract

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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 ${ℳ}_{G}^{d}\left(X\right)$ of the coarse moduli space for semistable principal $G$–bundles over $X$ is isomorphic to another component ${ℳ}_{{G}^{\prime }}^{{d}^{\prime }}\left({X}^{\prime }\right)$, then $X$ is isomorphic to ${X}^{\prime }$.

## How to cite

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Biswas, Indranil, and Hoffmann, Norbert. "A Torelli theorem for moduli spaces of principal bundles over a curve." Annales de l’institut Fourier 62.1 (2012): 87-106. <http://eudml.org/doc/251029>.

@article{Biswas2012,
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 $X^\{\prime\}$.},
affiliation = {School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India; Freie Universität Berlin, Institut fûr Mathematik, Arnimallee 3, 14195 Berlin, Germany},
author = {Biswas, Indranil, Hoffmann, Norbert},
journal = {Annales de l’institut Fourier},
keywords = {Principal bundle; moduli space; Torelli theorem; principal bundle},
language = {eng},
number = {1},
pages = {87-106},
publisher = {Association des Annales de l’institut Fourier},
title = {A Torelli theorem for moduli spaces of principal bundles over a curve},
url = {http://eudml.org/doc/251029},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Biswas, Indranil
AU - Hoffmann, Norbert
TI - A Torelli theorem for moduli spaces of principal bundles over a curve
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 1
SP - 87
EP - 106
AB - 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 $X^{\prime}$.
LA - eng
KW - Principal bundle; moduli space; Torelli theorem; principal bundle
UR - http://eudml.org/doc/251029
ER -

## References

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