Semiorthogonal decompositions in algebraic geometry

By Alexander Kuznetsov. 2014

155 citations recorded by the source corpus.

In this review we discuss what is known about semiorthogonal decompositions of derived categories of algebraic varieties. We review existing constructions, especially the homological projective duality approach, and discuss some related issues such as categorical resolutions of singularities.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/16bdba9226c201c6cad6f088dd944c1b9636ff4d

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Non-commutative resolutions of quotient singularities for reductive groups (2015, unknown): “e resolution is crepant if S is in addition Gorenstein and Λ is a maximal Cohen-Macaulay S-module. Among other things NCRs are a crucial part of the Kuznetsov’s Homological Projective Duality program [25, 26]. The HPD dual of a smooth projective variety is often a NCR (possibly twisted, see below) o”
Hilbert schemes of lines and conics and automorphism groups of Fano threefolds (2016, methodology): “generator of Pic(X), and by L X and P X the classes of a line and a point in the corresponding Chow or cohomology groups. The bounded derived category of coherent sheaves on Xis denoted by Db(X), see [Kuz14] for a recent survey. The main goal of this section is to prove Theorem 2.3.5. Besides, we gi”