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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Abstract
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 |
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Status: | Published |
Refereed: | Yes |
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: | 1465-3060 |
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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