Basepoint-freeness thresholds and higher syzygies on abelian threefolds.

For a polarized abelian variety, Z. Jiang and G. Pareschi introduced an invariant and showed that the polarization is basepoint-free or projectively normal if the invariant is small. Their result was generalized to higher syzygies by F. Caucci; that is, the polarization satisfies property (N_p) if the invariant is small. In this paper, we study a relation between the invariant and degrees of abelian subvarieties with respect to the polarization. For abelian threefolds, we give an upper bound of the invariant using degrees of abelian subvarieties. In particular, we affirmatively answer some questions on abelian varieties asked by the author, V. Lozovanu and F. Caucci in the three-dimensional case. [ABSTRACT FROM AUTHOR]