1994/12/23 by Roberto Scognamillo, R. Scognamillo, Scognamillo, R. · 2 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9412020
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)
openalex publication_date 1994/12/23 · arxiv created 1996/07/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Bn n>0, or when the commutator subgroup (G,G) is simply connected the map F is injective.