VOL. 88 | 2023 Stability over cDV singularities and other complete local rings
Okke van Garderen

Editor(s) Yukari Ito, Akira Ishii, Osamu Iyama

Adv. Stud. Pure Math., 2023: 461-489 (2023) DOI: 10.2969/aspm/08810461


We characterise subcategories of semistable modules for noncommutative minimal models of compound Du Val singularities, including the non-isolated case. We find that the stability is controlled by an infinite polyhedral fan that stems from tilting theory, and which can be computed from the Dynkin diagram combinatorics of the minimal models found in the work of Iyama–Wemyss. In the isolated case, we moreover find an explicit description of the deformation theory of the stable modules in terms of factors of the endomorphism algebras of 2-term tilting complexes. To obtain these results we generalise a correspondence between 2-term silting theory and stability, which is known to hold for finite dimensional algebras, to the much broader setting of algebras over a complete local Noetherian base ring.


Published: 1 January 2023
First available in Project Euclid: 8 May 2023

Digital Object Identifier: 10.2969/aspm/08810461

Primary: 14A22 , 16G30
Secondary: 16E35

Keywords: compound Du Val singularities , noncommutative algebraic geometry , representation theory , silting theory , stability conditions

Rights: Copyright © 2023 Mathematical Society of Japan


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