2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67709In 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.20 pages; new section on pluricanonical maps on varieties of maximal Albanese dimension added, mistake in the section on Picard bundles corrected, a few expository changes, some references addedAlgebraic Geometry14K05; 14H40text