Categorical joins

Kuznetsov, Alexander; Perry, Alexander

doi:10.1090/jams/963

Categorical joins
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by Alexander Kuznetsov and Alexander Perry;

J. Amer. Math. Soc. 34 (2021), 505-564

DOI: https://doi.org/10.1090/jams/963

Published electronically: February 18, 2021

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Abstract:

We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical projective duality. Our main theorem says that the homological projective dual category of the categorical join is naturally equivalent to the categorical join of the homological projective dual categories. This categorifies the classical version of this assertion and has many applications, including a nonlinear version of the main theorem of homological projective duality.

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