Faithful actions from hyperplane arrangements

Hirano, Y. and Wemyss, M. (2018) Faithful actions from hyperplane arrangements. Geometry and Topology, 22(6), pp. 3395-3433. (doi: 10.2140/gt.2018.22.3395)

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We show that if X is a smooth quasiprojective 3–fold admitting a flopping contraction, then the fundamental group of an associated simplicial hyperplane arrangement acts faithfully on the derived category of X. The main technical advance is to use torsion pairs as an efficient mechanism to track various objects under iterations of the flop functor (or mutation functor). This allows us to relate compositions of the flop functor (or mutation functor) to the theory of Deligne normal form, and to give a criterion for when a finite composition of 3–fold flops can be understood as a tilt at a single torsion pair. We also use this technique to give a simplified proof of a result of Brav and Thomas (Math. Ann. 351 (2011) 1005–1017) for Kleinian singularities.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Wemyss, Professor Michael
Authors: Hirano, Y., and Wemyss, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Geometry and Topology
Publisher:Mathematical Sciences Publishers
ISSN (Online):1364-0380
Published Online:23 September 2018
Copyright Holders:Copyright © 2018 Mathematical Sciences Publishers
First Published:First published in Geometry and Topology 22(6):3395-3433
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
756641The Homological Minimal Model ProgramMichael WemyssEngineering and Physical Sciences Research Council (EPSRC)EP/K021400/2M&S - MATHEMATICS