Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Homological projective duality for quadrics


Authors: Alexander Kuznetsov and Alexander Perry
Journal: J. Algebraic Geom.
DOI: https://doi.org/10.1090/jag/767
Published electronically: January 15, 2021
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Abstract | References | Additional Information

Abstract: 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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Additional Information

Alexander Kuznetsov
Affiliation: Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkin str., Moscow 119991 Russia; and National Research University Higher School of Economics, Moscow, Russia
Email: akuznet@mi-ras.ru

Alexander Perry
Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
Email: aperry@math.columbia.edu

DOI: https://doi.org/10.1090/jag/767
Received by editor(s): March 4, 2019
Published electronically: January 15, 2021
Additional Notes: The first author was partially supported by the HSE University Basic Research Program, Russian Academic Excellence Project “5-100”. The second author was partially supported by NSF postdoctoral fellowship DMS-1606460, NSF grant DMS-1902060, and the Institute for Advanced Study.