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All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces
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Title: | All 81 crepant resolutions of a finite quotient singularity are hyperpolygon spaces |
Authors: | Bellamy, G Craw, A Rayan, S Schedler, T Weiss, H |
Item Type: | Journal Article |
Abstract: | We demonstrate that the linear quotient singularity for the exceptional subgroup G in Sp(4, C) of order 32 is isomorphic to an affine quiver variety for a 5-pointed star-shaped quiver. This allows us to construct uniformly all 81 projective crepant resolutions of C4/G as hyperpolygon spaces by variation of GIT quotient, and we describe both the movable cone and the Namikawa Weyl group action via an explicit hyperplane arrangement. More generally, for the n-pointed star shaped quiver, we describe completely the birational geometry for the corresponding hyperpolygon spaces in dimension 2n − 6; for example, we show that there are 1684 projective crepant resolutions when n = 6. We also prove that the resulting affine cones are not quotient singularities for n ≥ 6. |
Issue Date: | 1-Apr-2024 |
Date of Acceptance: | 6-Nov-2023 |
URI: | http://hdl.handle.net/10044/1/108094 |
DOI: | 10.1090/jag/827 |
ISSN: | 1056-3911 |
Publisher: | American Mathematical Society |
Start Page: | 757 |
End Page: | 793 |
Journal / Book Title: | Journal of Algebraic Geometry |
Volume: | 33 |
Copyright Statement: | © Copyright 2024 University Press, Inc. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Publication Status: | Published |
Online Publication Date: | 2024-04-01 |
Appears in Collections: | Pure Mathematics Faculty of Natural Sciences Mathematics |
This item is licensed under a Creative Commons License