Hyperplane sections and derived categories

By Alexander Kuznetsov. 2005

207 citations recorded by the source corpus.

We give a generalization of the theorem of Bondal and Orlov about the derived categories of coherent sheaves on intersections of quadrics revealing its relation to projective duality. As an application we describe the derived categories of coherent sheaves on Fano 3-folds of index 1 and degrees 12, 16 and 18.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f0c47ce9ea82658781b617214503c25751edfc88

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Hilbert schemes of lines and conics and automorphism groups of Fano threefolds (2016, background): “Proposition 3.10] we have V _˘= (U X ); where U X is the restriction of the tautological bundle from LGr(3;6) to X (see also Remark B.1.4), : D b() !D (X) is the fully faithful functor constructed in [Kuz06b], and is its left adjoint functor (see [BF13] for details). Thus we have Hom(V ;V ) ˘= Hom(V”
Derived categories of Fano threefolds (2008, unknown): “They have the following explicit description: • X22 ⊂ P 13 is the zero locus of a global section of the vector bundle Λ2U∗ ⊕ Λ2U∗ ⊕ Λ2U∗ on the Grassmannian Gr(3, 7), where U denotes the tautological rank 3 bundle; • X18 = G2Gr(2, 7) ∩ P 11 ⊂ P13, where G2Gr(2, 7) is the minimal compact homogeneous ”
Lefschetz decompositions and categorical resolutions of singularities (2006, background): “A vector bundle E on X is said to be exceptional over S if it has nite Tor-dimension over S (see [ 13 ]) and f (E E) =OS.”
Derived categories of coherent sheaves (2006, background): “n classical algebraic geometry. The theory also leads to some extremely interesting derived equivalences between non-commutative varieties. For more details we refer the reader to the original papers [31, 32, 33, 34]. Acknowledgements. I’m very grateful to Antony Maciocia for teaching me about deriv”