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
Pareschi, G., Popa, M. (2011). Regularity on Abelian Varieties III: Relationship with Generic Vanishing and Applications. In D. Ellwood, E. Previato (a cura di), Grassmannians, Moduli Spaces and Vector Bundles (pp. 141-168). American Mathematical Society.
Regularity on Abelian Varieties III: Relationship with Generic Vanishing and Applications
PARESCHI, GIUSEPPE;
2011-01-01
Abstract
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| File | Dimensione | Formato | |
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