Generic vanishing filtrations and perverse objects in derived categories of coherent sheaves

Details Generic vanishing filtrations and perverse objects in derived categories of coherent sheaves Generic vanishing filtrations and perverse objects in derived categories of coherent sheaves

2009-11-18

arxiv.org/abs/0911.3648v2

Mathematics

Algebraic Geometry

22 pages; corrected [ABe] reference on first page; also the filtration on perverse sheaves in section 5 stabilizes to maximal

Scientific paper

This is a mostly expository paper, intended to explain a very natural relationship between two a priori distinct notions appearing in the literature: Generic Vanishing in the context of vanishing theorems and birational geometry, and Perverse Coherent Sheaves in the context of derived categories. I describe homological and commutative algebra criteria for checking either condition, and then recall applications to geometric situations. A few new results, and especially new proofs, are included as well.

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