Derived categories of noncommutative quadrics and Hilbert squares

Belmans, P. and Raedschelders, T. (2018) Derived categories of noncommutative quadrics and Hilbert squares. International Mathematics Research Notices, (doi: 10.1093/imrn/rny192) (Early Online Publication)

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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.

Item Type:Articles
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Raedschelders, Mr Theo
Authors: Belmans, P., and Raedschelders, T.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Mathematics Research Notices
Publisher:Oxford University Press
ISSN:1073-7928
ISSN (Online):1687-0247
Published Online:16 August 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in International Mathematics Research Notices 2018
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
3014430Reductions and Resolutions in representation theory and algebraic geometryTheo RaedscheldersEngineering and Physical Sciences Research Council (EPSRC)EP/R005214/1M&S - Mathematics