Regularity on Abelian Varieties III: Relationship with Generic Vanishing and Applications

By Giuseppe Pareschi, Mihnea Cristian Popa. 2008

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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

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cc4ae3df38a80df624e26142bbe195946ebb0bb7