Exceptional collections and window categories

Abstract: The derived category of a variety is a crucial algebraic invariant with several profound implications on the geometry of the underlying variety. This talk will focus on a particular structure of derived categories called a full exceptional collection. We will discuss the landscape of full exceptional collections and its connections to geometry, then explore how to produce them for linear GIT quotients using ideas from "window" categories and equivariant geometry. As an example, we will consider a large class of linear GIT quotients by a reductive group of rank two, where this machinery produces full exceptional collections consisting of tautological vector bundles. This talk is based on joint work with Daniel Halpern-Leistner.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html