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

TL;DR

This paper explains the relationship between Generic Vanishing theorems and Perverse Coherent Sheaves, providing criteria, applications, and new insights in the context of derived categories of coherent sheaves.

Contribution

It clarifies the connection between two important concepts in algebraic geometry and introduces new proofs and results related to their interplay.

Findings

Homological and algebraic criteria for checking Generic Vanishing and Perverse Sheaves.

Applications of these concepts to geometric situations.

New proofs and some new results in the area.

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.