Hyperplane sections and derived categories

Abstract

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.

76 pages

Cited by in corpus (16)

• Hilbert schemes of lines and conics and automorphism groups of Fano threefolds
• Calabi-Yau and fractional Calabi-Yau categories
• Derived categories of Gushel-Mukai varieties
• Derived categories of curves as components of Fano manifolds
• Fibrations in complete intersections of quadrics, Clifford algebras, derived categories, and rationality problems
• Cremona transformations and derived equivalences of K3 surfaces
• Exceptional collections, and the Neron-Severi lattice for surfaces
• Derived categories of cyclic covers and their branch divisors
• Derived equivalence of Ito-Miura-Okawa-Ueda Calabi-Yau 3-folds
• Hodge level for weighted complete intersections
• Perverse sheaves of categories and some applications
• Equivalence of K3 surfaces from Verra threefolds
• Derived categories of the Cayley plane and the coadjoint Grassmannian of type F
• Derived Categories of Grassmannians: a Survey
• A note on semiorthogonal decompositions for Fano fibrations
• A Semi-orthogonal Sequence in the Derived Category of the Hilbert Scheme of Three Points