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Triangulated categories of singularities and equivalences between Landau-Ginzburg models. (English) Zbl 1161.14301

Sb. Math. 197, No. 12, 1827-1840 (2006); translation from Mat. Sb. 197, No. 12, 117-132 (2006).
Summary: The existence of a certain type of equivalence between triangulated categories of singularities for varieties of different dimensions is proved. This class of equivalences generalizes the so-called Knörrer periodicity. As a consequence, equivalences between the categories of \(D\)-branes of type \(B\) on Landau-Ginzburg models of different dimensions are obtained.

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
18E30 Derived categories, triangulated categories (MSC2010)
14B05 Singularities in algebraic geometry
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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