Dimensions of Prym varieties (Q5945778)

Summary: Given a tame Galois branched cover of curves \(\pi:X\to Y\) with finite Galois group \(G\) whose representations are rational, we compute the dimension of the (generalized) Prym variety \(\text{Prym}_\rho(X)\) corresponding to each irreducible representation \(\rho\) 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.