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A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles

Published online by Cambridge University Press:  16 November 2020

David Favero ,
Daniel Kaplan  and
Tyler L. Kelly
David Favero
Affiliation:
University of Alberta, Department of Mathematical and Statistical Sciences, Central Academic Building 632, Edmonton, AB, Canada T6G 2C7 Korea Institute for Advanced Study, 85 Hoegiro, Dongdaemun-gu, Seoul, Republic of Korea 02455; E-mail: favero@ualberta.ca
Daniel Kaplan
Affiliation:
University of Birmingham, School of Mathematics, Birmingham B15 2TT, United Kingdom; E-mail: d.kaplan@bham.ac.uk
Tyler L. Kelly
Affiliation:
University of Birmingham, School of Mathematics, Birmingham B15 2TT, United Kingdom; E-mail: t.kelly.1@bham.ac.uk

Abstract

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We show that there exists a cubic threefold defined by an invertible polynomial that, when quotiented by the maximal diagonal symmetry group, has a derived category that does not have a full exceptional collection consisting of line bundles. This provides a counterexample to a conjecture of Lekili and Ueda.

Keywords

exceptional collectionsderived categoriestilting object
Type
Algebra
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e56
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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