Giuseppe Pareschi, Mihnea Popa
Published 2008-02-07, updated 2008-08-18Version 2
We describe the relationship between the notions of $M$-regular sheaf and $GV$-sheaf in the case of abelian varieties. The former is a natural strengthening of the latter, and we provide an algebraic criterion characterizing it among the larger class. Based on this we deduce new basic properties of both $M$-regular and $GV$-sheaves. In the second part we give a number of applications of generation criteria for $M$-regular sheaves to the study of Seshadri constants, Picard bundles, pluricanonical maps on irregular varieties, and semihomogeneous vector bundles. This second part of the paper is based on our earlier preprint math.AG/0306103, with some improved statements and shortened arguments.
Comments: 25 pages; this replaces the older preprint math.AG/0306103 and roughly half of the content is new; prepared for the Proceedings of the Clay Institute Workshop on vector bundles, October 2006; updated references
Regularity on abelian varieties III: further applications
Abelian varieties with group action
Regularity on abelian varieties II: basic results on linear series and defining equations
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