Equivalences of derived factorization categories of gauged Landau-Ginzburg models

Yuki Hirano

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arXiv · 1506.00177

Equivalences of derived factorization categories of gauged Landau-Ginzburg models

Yuki Hirano

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Abstract

For a given Fourier-Mukai equivalence of bounded derived categories of coherent sheaves on smooth quasi-projective varieties, we construct Fourier-Mukai equivalences of derived factorization categories of gauged Landau-Ginzburg (LG) models. As an application, we obtain some equivalences of derived factorization categories of K-equivalent gauged LG models. This result is an equivariant version of the result of Baranovsky and Pecharich, and it also gives a partial answer to Segal's conjecture. As another application, we prove that if the kernel of the Fourier-Mukai equivalence is linearizable with respect to a reductive affine algebraic group action, then the derived categories of equivariant coherent sheaves on the varieties are equivalent. This result is shown by Ploog for finite groups case.

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Yuki Hirano. 2015-05-30. Equivalences of derived factorization categories of gauged Landau-Ginzburg models. https://arxiv.org/abs/1506.00177

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