Triangulated categories of singularities and equivalences between Landau-Ginzburg models

By Dmitri Orlov. 2005

186 citations recorded by the source corpus.

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 Knorrer periodicity. As a consequence, equivalences between the categories of D-branes of type B on Landau-Ginzburg models of different dimensions are obtained.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/25abfe33c3460d63f1b9695695f3dfc15da1e2c7

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Lefschetz decompositions and categorical resolutions of singularities (2006, background): “perfect complexes in D(Y,A) is denoted by Dperf(Y,A). It is a triangulated subcategory of D(Y,A). Perfect complexes in Db(Y ) can be characterized intrinsically by the following property. Lemma 2.10 ([O2], Pr. 1.11). An object F ∈ Db(Y) is a perfect complex if and only if for any G ∈ Db(Y) there exi”
Singularity Categories, Schur Functors and Triangular Matrix Rings (2007, unknown): “The singularity category [13–15] of R is defined to be the following Verdier quotient category”
Lagrangian fibrations on blowups of toric varieties and mirror symmetry for hypersurfaces (2012, methodology): “in the sense of Orlov’s generalized Knörrer periodicity [36]) to the Landau-Ginzburg model consisting of g(0) = {(z1, .”
Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities (2005, background): “− · ··} of coherent sheaves in which the composition of differentials is no longer zero, but is equal to multiplication by W (see, e.g., [17, 22, 23 ]).”
Towards Mirror Symmetry for Varieties of General Type (2012, background): “ve line in this setup would be (x+y+z: Bl0 A3 →C) ↔(x+y+z+xyz: A3 →C). This turns into the usual pair P1 ↔x+ 1/x: C∗ →C by the transition to the critical locus on the left and via Knorrer periodicity [Or05] on the right. This works by writing the potential as x+y+z(1+xy) = w+fgand taking for the new”
Matrix factorizations for nonaffine LG–models (2011, background): “It is proved in [ 9 ] that if a scheme X satisfies (ELF).”