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arXiv · 2009.12785

Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations

Yuki Hirano
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Abstract

We show that equivariant tilting modules over equivariant algebras induce equivalences of derived factorization categories. As an application, we show that the derived category of a noncommutative resolution of a linear section of a Pfaffian variety is equivalent to the derived factorization category of a noncommutative gauged Landau-Ginzburg model $(\Lambda,\chi, w)^{\mathbb{G}_m}$, where $\Lambda$ is a noncommutative resolution of the quotient singularity $W/\operatorname{GSp}(Q)$ arising from a certain representation $W$ of the symplectic similitude group $\operatorname{GSp}(Q)$ of a symplectic vector space $Q$.

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Yuki Hirano. 2020-09-27. Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations. https://doi.org/10.3842/sigma.2021.055

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