TL;DR
This paper explores the development of Homological Projective Duality, starting from foundational theorems and illustrating its applications through various examples.
Contribution
It provides a conceptual overview connecting classical theorems to Kuznetsov's Homological Projective Duality and surveys key examples.
Findings
Connections between Beilinson and Orlov theorems and HPD
Illustrative examples of HPD applications
Clarification of the theoretical framework
Abstract
Beginning with the theorems of Beilinson and Orlov on derived categories, we show how these lead naturally to Kuznetsov's beautiful theory of Homological Projective Duality. We then survey some examples.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory