Mixed Braid Group Actions From Deformations of Surface Singularities

Will Donovan*, Ed Segal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a set of toric Calabi–Yau varieties which arise as deformations of the small resolutions of type A surface singularities. By careful analysis of the heuristics of B-brane transport in the associated gauged linear sigma models, we predict the existence of a mixed braid group action on the derived category of each variety, and then prove that this action does indeed exist. This generalizes the braid group action found by Seidel and Thomas for the undeformed resolutions. We also show that the actions for different deformations are related, in a way that is predicted by the physical heuristics.

Original languageEnglish
Pages (from-to)497-543
JournalCommunications in Mathematical Physics
Volume335
Issue number1
Early online date4 Dec 2014
DOIs
Publication statusPublished - Apr 2015

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