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)

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

Related URLs

• arXiv