Characteristic classes and stability conditions for projective Kleinian orbisurfaces

Lim, B. and Rota, F. (2022) Characteristic classes and stability conditions for projective Kleinian orbisurfaces. Mathematische Zeitschrift, 300(1), pp. 827-849. (doi: 10.1007/s00209-021-02805-8)

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Abstract

We construct Bridgeland stability conditions on the derived category of smooth quasi-projective Deligne–Mumford surfaces whose coarse moduli spaces have ADE singularities. This unifies the construction for smooth surfaces and Bridgeland’s work on Kleinian singularities. The construction hinges on an orbifold version of the Bogomolov–Gieseker inequality for slope semistable sheaves on the stack, and makes use of the Toën–Hirzebruch–Riemann–Roch theorem.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Rota, Dr Franco
Authors: Lim, B., and Rota, F.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Mathematische Zeitschrift
Publisher:Springer
ISSN:0025-5874
ISSN (Online):1432-1823
Published Online:13 July 2021
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Mathematische Zeitschrift 300(1): 827-849
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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