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See detailHomological projective duality for the Segre cubic
Beckmann, Thorsten; Belmans, Pieter UL

E-print/Working paper (2022)

The Segre cubic and Castelnuovo-Richmond quartic are two projectively dual hypersurfaces in P^4, with a long and rich history starting in the 19th century. We will explain how Kuznetsov's theory of ... [more ▼]

The Segre cubic and Castelnuovo-Richmond quartic are two projectively dual hypersurfaces in P^4, with a long and rich history starting in the 19th century. We will explain how Kuznetsov's theory of homological projective duality lifts this projective duality to a relationship between the derived category of a small resolution of the Segre cubic and a small resolution of the Coble fourfold, the double cover of P^4 ramified along the Castelnuovo-Richmond quartic. Homological projective duality then provides a description of the derived categories of linear sections, which we will describe to illustrate the theory. The case of the Segre cubic and Coble fourfold is non-trivial enough to exhibit interesting behavior, whilst being easy enough to explain the general machinery in this special and very classical case. [less ▲]

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