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Revisiting the moduli space of semistable G-bundles over elliptic curves

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Fratila,  Dragos
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Fratila, D. (2021). Revisiting the moduli space of semistable G-bundles over elliptic curves. Annales de l'Institut Fourier, 71(2), 615-641. doi:10.5802/aif.3405.


Cite as: https://hdl.handle.net/21.11116/0000-000B-6845-3
Abstract
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.