Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities
Abstract
In this paper we establish an equivalence between the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W and the triangulated category of singularities of the fiber of W over zero. The main result is a theorem that shows that the graded triangulated category of singularities of the cone over a projective variety is connected via a fully faithful functor to the bounded derived category of coherent sheaves on the base of the cone. This implies that the category of graded D-branes of type B in Landau-Ginzburg models with homogeneous superpotential W is connected via a fully faithful functor to the derived category of coherent sheaves on the projective variety defined by the equation W=0.
Keywords
Cite
@article{arxiv.math/0503632,
title = {Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities},
author = {Dmitri Orlov},
journal= {arXiv preprint arXiv:math/0503632},
year = {2018}
}
Comments
26 pp., LaTeX