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

Zhang, Lei

doi:10.1090/S0002-9939-2014-11982-4

A note on the linear systems on the projective bundles over Abelian varieties
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Proc. Amer. Math. Soc. 142 (2014), 2569-2580 Request permission

Abstract:

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

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