An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups
| dc.creator | Scognamillo, R. | |
| dc.date | 1994-12-23 | |
| dc.date | 1996-07-09 | |
| dc.date.accessioned | 2026-07-07T08:57:55Z | |
| dc.date.available | 2026-07-07T08:57:55Z | |
| dc.description | 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. | |
| dc.description | 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) | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9412020 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9412020 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/147120 | |
| dc.subject | Algebraic Geometry | |
| dc.title | An elementary approach to the abelianization of the Hitchin system for arbitrary reductive groups | |
| dc.type | text |