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Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities

  • Dmitri Orlov
Chapter
Part of the Progress in Mathematics book series (PM, volume 270)

Summary

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.

Key words

Triangulated categories of singularities derived categories of coherent sheaves branes Landau–Ginzburg models 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Algebra SectionSteklov Mathematical Institute RANMoscowRUSSIA

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