Semiorthogonal decompositions in algebraic geometry
Alexander Kuznetsov
TL;DR
This paper reviews the current understanding of semiorthogonal decompositions in algebraic geometry, focusing on their constructions, especially homological projective duality, and related topics like categorical resolutions.
Contribution
It provides a comprehensive overview of known methods and issues related to semiorthogonal decompositions in derived categories of algebraic varieties.
Findings
Summarizes existing constructions of semiorthogonal decompositions.
Discusses the homological projective duality approach.
Addresses categorical resolutions of singularities.
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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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology