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Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities

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Algebra, Arithmetic, and Geometry

Part of the book series: Progress in Mathematics ((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.

2000 Mathematics Subject Classifications: 18E30, 81T30, 14B05

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Authors and Affiliations

  1. Algebra Section, Steklov Mathematical Institute RAN, Gubkin str. 8, Moscow, 119991, RUSSIA

    Dmitri Orlov

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  1. Dmitri Orlov
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Correspondence to Dmitri Orlov .

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Editors and Affiliations

  1. Courant Inst. Mathematical, New York University, Mercer St. 251, New York, 10012, USA

    Yuri Tschinkel

  2. Eberly College of Science, Pennsylvania State University, University Park, 16802, USA

    Yuri Zarhin

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Dedicated to Yuri Ivanovich Manin on the occasion of his 70th birthday

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Orlov, D. (2009). Derived Categories of Coherent Sheaves and Triangulated Categories of Singularities. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 270. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4747-6_16

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