Principal N-bundles for n an extension of a finite group by an abelian group

摘要

Consider an extension 0 → T → N → W → 0 of a finite group W by an abelian group T. Let X be a smooth projective complex curve. Let M_X(N) denote the moduli space of principal N-bundles on the curve X. We give a precise description of the fiber of the quotient by T map q_τ: M_X(N) → M_X(W) as a torsor over an abelian variety, namely, the Prym-Donagi variety. We also prove a result on Mumford groups.