Matrix factorizations for nonaffine LG–models

By Dmitri Orlov. 2011

103 citations recorded by the source corpus.

We propose a natural definition of a category of matrix factorizations for nonaffine Landau–Ginzburg models. For any LG-model we construct a fully faithful functor from the category of matrix factorizations defined in this way to the triangulated category of singularities of the corresponding fiber. We also show that this functor is an equivalence if the total space of the LG-model is smooth.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f66dcc1efb04fd8068849e9319015018c0110aeb

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Homological mirror symmetry for punctured spheres (2011, background): “It is proved in [33] that there is an equivalence”
Coherent analogues of matrix factorizations and relative singularity categories (2011, background): “One generalizes the above definition, replacing free modules with projective modules [Kapustin and Li 2003; Orlov 2004], with locally free sheaves [Orlov 2012], and finally with coherent sheaves [Lin and Pomerleano 2013].”
The derived category of a GIT quotient (2012, result): “Note that by an equivariant generalization of [22], these results could be equivalently formulated in terms of categories of matrix factorizations.”
A Beginner’s Introduction to Fukaya Categories (2013, background): “While this conjecture was initially stated for compact Calabi-Yau manifolds (and recently proved for the quintic 3-fold by Sheridan [46]), it also holds (and is often easier to prove) for noncompact manifolds (in which case one should consider the wrapped Fukaya category), and outside of the Calabi-”