Understanding the flop-flop autoequivalence using spherical functors

05-Nov-2020, 13:30-14:30 (3 years ago)

Abstract: The homological interpretation of the Minimal Model Program conjectures that flips should correspond to embeddings of derived categories, and flops to equivalences. Even if the conjecture doesn’t provide us with a preferred functor, there is an obvious choice: the pull-push via the fibre product. When this approach work, we obtain an interesting autoequivalence of either side of the flop, known as the “flop-flop autoequivalence”. Understanding the structure of this functor (e.g. does it split as the composition of simpler functors?) is an interesting problem, and it has been extensively studied. In this talk I will explain that there is a natural, i.e. arising from the geometry, way to realise the “flop-flop autoequivalence” as the inverse of a spherical twist, and that this presentation can help us shed light on the structure of the autoequivalence itself.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )


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

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
*contact for this listing

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