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  Derived categories of noncommutative quadrics and Hilbert squares

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.

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arXiv:1605.02795.pdf (Preprint), 328KB
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Belmans-Raedschelders_Derived categories of noncommutative quadrics and Hilbert squares_2020.pdf (Publisher version), 848KB
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© The Author(s) 2018. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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 Creators:
Belmans, Pieter1, Author           
Raedschelders, Theo, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Algebraic Geometry, Quantum Algebra, Rings and Algebras, Representation Theory
 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.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 28
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1605.02795
DOI: 10.1093/imrn/rny192
 Degree: -

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Title: International Mathematics Research Notices
  Abbreviation : IMRN
Source Genre: Journal
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Publ. Info: Oxford University Press
Pages: - Volume / Issue: 2020 (19) Sequence Number: - Start / End Page: 6042 - 6069 Identifier: -