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

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

1994-12-23

arxiv.org/abs/alg-geom/9412020v3

Mathematics

Algebraic Geometry

25 pages, LaTex. In the revised version, the most relevant changes are in the proofs contained in section 3. The major ones co

Scientific paper

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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