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Categorical joins


Authors: Alexander Kuznetsov and Alexander Perry
Journal: J. Amer. Math. Soc. 34 (2021), 505-564
MSC (2020): Primary 14A22, 14F08, 14N05
DOI: https://doi.org/10.1090/jams/963
Published electronically: February 18, 2021
MathSciNet review: 4280866
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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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Additional Information

Alexander Kuznetsov
Affiliation: Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina str., Moscow 119991, Russia
MR Author ID: 359553
Email: akuznet@mi-ras.ru

Alexander Perry
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
MR Author ID: 907593
Email: arper@umich.edu

Received by editor(s): March 4, 2019
Received by editor(s) in revised form: March 21, 2019, April 8, 2020, and June 24, 2020
Published electronically: February 18, 2021
Additional Notes: The work of the first author was performed at the Steklov International Mathematical Center and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2019-1614).
The second author was partially supported by NSF postdoctoral fellowship DMS-1606460, NSF grant DMS-1902060/DMS-2002709, and the Institute for Advanced Study.
Article copyright: © Copyright 2021 American Mathematical Society