Regularity on abelian varieties III: further applications

TL;DR

This paper extends the theory of M-regularity on abelian varieties to new applications, including Seshadri constants, Picard bundles, pluricanonical maps, and semihomogeneous vector bundles, advancing the understanding of irregular varieties.

Contribution

It introduces novel applications of M-regularity theory to various geometric objects and maps on abelian and irregular varieties, building on previous work.

Findings

New bounds for Seshadri constants on abelian varieties

Characterization of Picard bundles using M-regularity

Insights into pluricanonical maps on irregular varieties

Abstract

In the present sequel to our previous two papers on regularity on abelian varieties, we give a number of new applications of the theory of $M$-regularity to the study of Seshadri constants, Picard bundles, pluricanonical maps on irregular varieties, and semihomogeneous vector bundles.