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Derived categories of noncommutative quadrics and Hilbert squares

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Belmans,  Pieter
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Belmans, P., & Raedschelders, T. (2020). Derived categories of noncommutative quadrics and Hilbert squares. International Mathematics Research Notices, 2020(19), 6042-6069. doi:10.1093/imrn/rny192.


Cite as: http://hdl.handle.net/21.11116/0000-0007-A127-7
Abstract
A noncommutative deformation of a quadric surface is usually described by a three-dimensional cubic Artin-Schelter regular algebra. In this paper we show that for such an algebra its bounded derived category embeds into the bounded derived category of a commutative deformation of the Hilbert scheme of two points on the quadric. This is the second example in support of a conjecture by Orlov. Based on this example, we formulate an infinitesimal version of the conjecture, and provide some evidence in the case of smooth projective surfaces.