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Article Dans Une Revue Pure and Applied Mathematics Quarterly Année : 2021

Graded tilting for gauged Landau-Ginzburg models and geometric applications

Résumé

In this paper we develop a graded tilting theory for gauged Landau-Ginzburg models of regular sections in vector bundles over projective varieties. Our main theoretical result describes - under certain conditions - the bounded derived category of the zero locus $Z(s)$ of such a section $s$ as a graded singularity category of a non-commutative quotient algebra $\Lambda/\langle s\rangle$: $D^b(\mathrm{coh} Z(s))\simeq D^{\mathrm{gr}}_{\mathrm{sg}}(\Lambda/\langle s\rangle)$. Our geometric applications all come from homogeneous gauged linear sigma models. In this case $\Lambda$ is a non-commutative resolution of the invariant ring which defines the $\mathbb{C}^*$-equivariant affine GIT quotient of the model. We obtain purely algebraic descriptions of the derived categories of the following families of varieties: - Complete intersections. - Isotropic symplectic and orthogonal Grassmannians. - Beauville-Donagi IHS 4-folds.

Dates et versions

hal-02283620 , version 1 (11-09-2019)

Identifiants

Citer

Christian Okonek, Andrei Teleman. Graded tilting for gauged Landau-Ginzburg models and geometric applications. Pure and Applied Mathematics Quarterly, 2021, 17 (1), pp.185-235. ⟨10.4310/PAMQ.2021.v17.n1.a5⟩. ⟨hal-02283620⟩
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