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Faithful actions from
hyperplane arrangements
Yuki Hirano and Michael Wemyss |
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Geometry & Topology 22 (2018) 3395–3433
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Abstract |
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We show that if is a smooth quasiprojective –fold admitting a flopping contraction, then the fundamental group of an associated simplicial hyperplane arrangement acts faithfully on the derived category of . 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 –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. |
Keywords
derived category, flopping contraction, Deligne groupoid
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Mathematical Subject Classification 2010
Primary: 18E30
Secondary: 14E30, 14F05, 14J30, 20F36
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References |
Publication
Received: 13 January 2017
Revised: 14 November 2017
Accepted: 31 December 2017
Published: 23 September 2018
Proposed: Richard Thomas
Seconded: Jim Bryan, Dan Abramovich
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Authors |
| Yuki Hirano | |
| Department of Mathematics Kyoto University Kyoto Japan |
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| Michael Wemyss | |
| School of Mathematics and
Statistics University of Glasgow Glasgow United Kingdom |
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