We show that over an algebraically closed field of characteristic not equal to 2, homological projective duality for smooth quadric hypersurfaces and for double covers of projective spaces branched over smooth quadric hypersurfaces is a combination of two operations: one interchanges a quadric hypersurface with its classical projective dual and the other interchanges a quadric hypersurface with the double cover branched along it.
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Categorical joins
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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- NSF-PAR ID:
- 10329187
- Date Published:
- Journal Name:
- Journal of the American Mathematical Society
- Volume:
- 34
- Issue:
- 2
- ISSN:
- 0894-0347
- Page Range / eLocation ID:
- 505 to 564
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1090/jams/963
