Singular derived categories of Q-factorial terminalizations and maximal modification algebras

Osamu Iyama, Michael Wemyss*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 D-sg(X) and its idempotent completion , 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 A is derived equivalent to X as above, then X is Q-factorial if and only if A 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. (c) 2014 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)85-121
Number of pages37
JournalAdvances in Mathematics
Volume261
DOIs
Publication statusPublished - 20 Aug 2014

Keywords

  • Minimal models
  • Noncommutative resolutions
  • CM modules
  • HYPERSURFACE SINGULARITIES
  • TRIANGULATED CATEGORIES
  • CANONICAL SINGULARITIES
  • LOCAL HYPERSURFACES
  • TILTING MODULES
  • PICARD-GROUPS
  • FLOPS
  • EQUIVALENCES
  • RESOLUTION
  • DIMENSION

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