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An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups

R. Scognamillo
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Abstract

We consider the moduli space of stable principal G-bundles over a compact Riemann surface C of genus >1, with G a reductive algebraic group. We explicitly construct a map F from the generic fibre of the Hitchin map to a generalized Prym variety associated to a suitable Galois covering of C. The map F has finite fibres. In case G=PGl(2) one can check that the generic fibre of F is a principal homogeneous space with respect to a product of 2d-2 copies of Z/2Z where d is the degree of the canonical bundle over C. However in case the Dynkin diagram of G does not contain components of type $B_{n}$ n>0, or when the commutator subgroup (G,G) is simply connected the map F is injective.

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BibTeXRIS

R. Scognamillo. 1996-07-09. An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups. https://arxiv.org/abs/alg-geom/9412020

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