On the noncommutative Bondal-Orlov conjecture for some toric varieties

Autor:	Špenko, Špela, Bergh, Michel Van den, Bell, with an appendix by Jason P.
Rok vydání:	2018
Předmět:	Mathematics - Algebraic Geometry Mathematics - Rings and Algebras
Druh dokumentu:	Working Paper
Popis:	We show that all toric noncommutative crepant resolutions (NCCRs) of affine GIT quotients of "weakly symmetric" unimodular torus representations are derived equivalent. This yields evidence for a non-commutative extension of a well known conjecture by Bondal and Orlov stating that all crepant resolutions of a Gorenstein singularity are derived equivalent. We prove our result by showing that all toric NCCRs of the affine GIT quotient are derived equivalent to a fixed Deligne-Mumford GIT quotient stack associated to a generic character of the torus. This extends a result by Halpern-Leistner and Sam which showed that such GIT quotient stacks are a geometric incarnation of a family of specific toric NCCRs constructed earlier by the authors. Comment: 13 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1804.02881 Zobrazit plný text záznamu View this record from Arxiv