A NOTE ON THE LINEAR SYSTEMS ON THE PROJECTIVE BUNDLES OVER ABELIAN VARIETIES

It is well known that for an ample line bundle L on an Abelian variety A, the linear system vertical bar 2L vertical bar is base point free and 3L is very ample; moreover, the map defined by the linear system vertical bar 2L vertical bar 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).