Theta Groups over Extensions of Abelian Varieties by Unipotent Groups

Abstract

[EN]Let 0 → K_U → Y → X → 0 be a sequence of morphisms of algebraic groups over an algebraically closed field k, where X is an abelian variety, K_U is a unipotent, connected and commutative group scheme, and (X, π) is a geometric quotient of Y by K_U.

If L is an invertible sheaf over X, in this paper we generalize to L' = π* L the notion of a theta group associated with an invertible sheaf given by D. Mumford for an abelian variety.