Thesis or Dissertation Derived Factorization Categories of Gauged Landau-Ginzburg Models

Hirano, Yuki

pp.1 - 79 , 2017-03-25
In the first half of this thesis, 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. In the second half, we prove a Knörrer periodicity type equivalence between derived factorization categories of gauged LG models, which is an analogy of a theorem proved by Shipman and Isik independently. As an application, we obtain a gauged LG version of Orlov's theorem describing a relationship between categories of graded matrix factorizations and derived categories of hypersurfaces in projective spaces, by combining the above Knorrer periodicity type equivalence and the theory of variations of GIT quotients due to Ballard, Favero and Katzarkov.
首都大学東京, 2017-03-25, 博士(理学)

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