Equivariant Tilting Modules, Pfaffian Varieties and Noncommutative Matrix Factorizations

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 $W/\mathrm{GSp}(Q)$ arising from a certain representation $W$ of the symplectic similitude group $\mathrm{GSp}(Q)$ of a symplectic vector space $Q$.

References in corpus (2)

• Combinatorial constructions of derived equivalences
• Graded tilting for gauged Landau-Ginzburg models and geometric applications