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Derived Knörrer periodicity and Orlov’s theorem for gauged Landau–Ginzburg models

Part of: (Co)homology theory Abelian categories

Published online by Cambridge University Press:  23 March 2017

Yuki Hirano
Yuki Hirano*
Affiliation:
Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minamiohsawa, Hachioji-shi, Tokyo, 192-0397, Japan email [email protected]
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Abstract

We prove a Knörrer-periodicity-type equivalence between derived factorization categories of gauged Landau–Ginzburg models, which is an analogy of a theorem proved by Shipman and Isik independently. As an application, we obtain a gauged Landau–Ginzburg 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 Knörrer periodicity type equivalence and the theory of variations of geometric invariant theory quotients due to Ballard, Favero and Katzarkov.

Keywords

derived factorization categoryKnörrer periodicity

MSC classification

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions
Secondary: 18E30: Derived categories, triangulated categories
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 5 , May 2017 , pp. 973 - 1007
Copyright
© The Author 2017 

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