Derived Knörrer periodicity and Orlov's theorem for gauged Landau–Ginzburg models. (23rd March 2017)

• Record Type: Journal Article
• Authors: Hirano, Yuki
• Is Part Of: Compositio mathematica. Volume 153:Number 5(2017)
• Page Start: 973
• Page End: 1007
• Publication Date: 2017-03-23
• Subjects: 14F05 (primary), -- 18E30 (secondary); derived factorization category, -- Knörrer periodicity; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X16008344
• Languages: English
• ISSNs: 0010-437X

Abstract

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.