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arXiv · 1810.10060

Noncommutative deformation theory, the derived quotient, and DG singularity categories

Matt Booth
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Abstract

We show that Braun-Chuang-Lazarev's derived quotient prorepresents a naturally defined noncommutative derived deformation functor. Given a noncommutative partial resolution of a Gorenstein algebra, we show that the associated derived quotient controls part of its dg singularity category. We use a recent result of Hua and Keller to prove a recovery theorem, which can be thought of as providing a solution to a derived enhancement of a conjecture made by Donovan and Wemyss about the birational geometry of threefold flops.

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Matt Booth. 2018-10-23. Noncommutative deformation theory, the derived quotient, and DG singularity categories. https://arxiv.org/abs/1810.10060

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