A note on the linear systems on the projective bundles over Abelian varieties

Abstract

It is well known that for an ample line bundle L L on an Abelian variety A A , the linear system | 2 L | |2L| is base point free and 3 L 3L is very ample; moreover, the map defined by the linear system | 2 L | |2L| is well understood (cf. Theorem 1.1). In this paper we generalize this classical result and give a new proof using the theory developed by Pareschi and Popa in 2011 (cf. Theorem 1.2).