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Mutations of noncommutative crepant resolutions in GIT

Introductory Workshop: Noncommutative Algebraic Geometry February 05, 2024 - February 09, 2024

February 09, 2024 (09:00 AM PST - 10:00 AM PST)
Speaker(s): Yuki Hirano (Tokyo University of Agriculture and Technology)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC

Mutations of noncommutative crepant resolutions in GIT


Noncommutative crepant resolutions (NCCR), introduced by Van den Bergh, are noncommutative analogue of crepant resolutions of singularities. An NCCR of a fixed singular variety is not unique in general, but it is known that all NCCRs of a fixed Gorenstein terminal 3-fold are related by certain transformations of them, which are called mutations. In this talk, we discuss mutations of NCCRs arising from quasi-symmetric torus representations, and  then we explain that a spherical twist on the derived category of a Calabi-Yau complete intersection corresponds to iterated mutations of NCCRs via noncommutative matrix factorizations. This talk is based on joint work with Wahei Hara.

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Mutations of noncommutative crepant resolutions in GIT

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