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International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 2, Pages 107-116
http://dx.doi.org/10.1155/S016117120101153X

Dimensions of Prym varieties

Mathematics Department, State University of New York at Stony Brook, Stony Brook 11794, NY, USA

Received 22 January 2001

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Given a tame Galois branched cover of curves π:XY with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety Prymρ(X) corresponding to any irreducible representation ρ of G. This formula can be applied to the study of algebraic integrable systems using Lax pairs, in particular systems associated with Seiberg-Witten theory. However, the formula is much more general and its computation and proof are entirely algebraic.