International Journal of Mathematics and Mathematical Sciences
Volume 26 (2001), Issue 2, Pages 107-116
doi: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 Amy E. Ksir. 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: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.