Semi-orthogonal decompositions and discriminants

Abstract: The derived category of a toric variety can usually be decomposed into smaller pieces, by passing through different birational models and applying the "windows" theory relating VGIT and derived categories. There are many choices involved and the decompositions are not unique. We prove a Jordan-Hölder result, that the multiplicities of the pieces are independent of choices. If the toric variety is Calabi-Yau then there are no decompositions, instead the theory produces symmetries of the derived category. Physics predicts that these all these symmetries form an action of the fundamental group of the "FI parameter space". I'll explain why our Jordan-Hölder result is necessary for this prediction to work, and state a conjecture (based on earlier work of Aspinwall-Plesser-Wang) relating our multiplicities to the geometry of the FI parameter space. This is joint work with Alex Kite.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

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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

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