English

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

Algebraic Geometry 2009-11-23 v2 Commutative Algebra

Abstract

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.

Keywords

Cite

@article{arxiv.0911.3648,
  title  = {Generic vanishing filtrations and perverse objects in derived categories of coherent sheaves},
  author = {Mihnea Popa},
  journal= {arXiv preprint arXiv:0911.3648},
  year   = {2009}
}

Comments

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