An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups
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 n>0, or when the commutator subgroup (G,G) is simply connected the map F is injective.
Cite
@article{arxiv.alg-geom/9412020,
title = {An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups},
author = {R. Scognamillo},
journal= {arXiv preprint arXiv:alg-geom/9412020},
year = {2008}
}
Comments
25 pages, LaTex. In the revised version, the most relevant changes are in the proofs contained in section 3. The major ones concern the proof of theorem 3.2 (theorem 3.1 in the revised version)