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

Dimensions of Prym varieties

Abstract

Given a tame Galois branched cover of curves π:X→Y 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.