On symplectic resolutions and factoriality of Hamiltonian reductions

Bellamy, G. and Schedler, T. (2019) On symplectic resolutions and factoriality of Hamiltonian reductions. Mathematische Annalen, 375(1-2), pp. 165-176. (doi: 10.1007/s00208-019-01851-2)

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Recently, Herbig--Schwarz--Seaton have shown that 3-large representations of a reductive group G give rise to a large class of symplectic singularities via Hamiltonian reduction. We show that these singularities are always terminal. We show that they are Q-factorial if and only if G has finite abelianization. When G is connected and semi-simple, we show they are actually locally factorial. As a consequence, the symplectic singularities do not admit symplectic resolutions when G is semi-simple. We end with some open questions.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bellamy, Professor Gwyn
Authors: Bellamy, G., and Schedler, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Mathematische Annalen
ISSN (Online):1432-1807
Published Online:14 June 2019
Copyright Holders:Copyright © 2019 The Authors
First Published:First published in Mathematische Annalen 375(1-2):165-176
Publisher Policy:Reproduced under a Creative Commons License
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