On Seshadri constants of non-simple abelian varieties
Abstract
We prove that the Seshadri constant of a polarized abelian variety is equal to the Seshadri constant of its abelian subvariety if the Seshadri constant is relatively small with respect to its degree, or it contains an abelian divisor which has sufficiently small degree. As an application of these results, we show that the Seshadri constant of a polarized abelian surface is computed by the unique Seshadri curve if the Seshadri constant is small enough. As another application, we compute the Seshadri constants of some non-simple polarized abelian threefolds which contain principally polarized abelian surfaces.
Keywords
Cite
@article{arxiv.1909.13461,
title = {On Seshadri constants of non-simple abelian varieties},
author = {Rikito Ohta},
journal= {arXiv preprint arXiv:1909.13461},
year = {2022}
}
Comments
Section 2 in the previous version are omitted and its contents are included in the introduction in Section 1. Some trivial results are omitted from the applications in Section 3. final version