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The map defined by a non-very ample line bundle on an irregular variety

In this paper, we studied the map defined by a non-very ample line bundle on some special irregular varieties. As to this topic, it is well known that for a 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 \ref{oldth}). First, we generalized this classical result to projective bundles over Abelian varieties (cf. Theorem \ref{key}). Then we studied the bicanonical map of an irregular primitive variety $X$ of general type with $dim(X) = q(X)$, in fact we got a relation between the map and the reducibility of a divisor.