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A geometric presentation of the flop-flop autoequivalence as a(n inverse) spherical twist

Banff International Research Station for Mathematical Innovation and Discovery

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 doesnâ 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 â flop-flop autoequivalenceâ . 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 â flop-flop autoequivalenceâ as the inverse of a spherical twist, and that this presentation can help us shed light on the structure of the autoequivalence itself.

Mathematics; Algebraic geometry; Category theory; homological algebra

video/mp4

Author affiliation: UCL

2021-05-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/78076

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/