Semiorthogonal decompositions in algebraic geometry

2014/04/11 by Kuznetsov, Alexander · 5 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.3143

Abstract

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.

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• Derived categories of Gushel-Mukai surfaces and Fano fourfolds of K3 type
• Deformation theory for a morphism in the derived category with fixed lift of the codomain
• A new phantom on a rational surface
• Prime Fano 4-folds with semi-free torus actions
• Admissible subcategories supported on curves

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