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.

26 pp., LaTeX

References in corpus (3)

• F-term equations near Gepner points
• Triangulated categories of singularities and equivalences between Landau-Ginzburg models
• Matrix Factorizations and Representations of Quivers I

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