Singular derived categories of -factorial terminalizations and maximal modification algebras

Iyama, O. and Wemyss, M. (2014) Singular derived categories of -factorial terminalizations and maximal modification algebras. Advances in Mathematics, 261, pp. 85-121. (doi: 10.1016/j.aim.2014.04.001)

Abstract

Let X be a Gorenstein normal 3-fold satisfying (ELF) with local rings which are at worst isolated hypersurface (e.g. terminal) singularities. By using the singular derived category Dsg(X) and its idempotent completion View the MathML source, we give necessary and sufficient categorical conditions for X to be Q-factorial and complete locally Q-factorial respectively. We then relate this information to maximal modification algebras (= MMAs), introduced in [20], by showing that if an algebra Λ is derived equivalent to X as above, then X is Q-factorial if and only if Λ is an MMA. Thus all rings derived equivalent to Q-factorial terminalizations in dimension three are MMAs. As an application, we extend some of the algebraic results in [6] and [14] using geometric arguments.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Wemyss, Professor Michael
• Authors: Iyama, O., and Wemyss, M.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Advances in Mathematics
• Publisher: Elsevier
• ISSN: 0001-8708
• ISSN (Online): 1090-2082
• Published Online: 20 May 2014
• Copyright Holders: Copyright © 2014 Elsevier, Inc.
• First Published: First published in Advances in Mathematics 261:85-121
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher