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

David Favero; Daniel Kaplan; Tyler L. Kelly

doi:10.1017/fms.2020.44

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

David Favero, Daniel Kaplan, Tyler L. Kelly

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English (US)
Journal	Forum of Mathematics, Sigma
DOIs	https://doi.org/10.1017/fms.2020.44
State	Accepted/In press - 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© The Author(s), 2020. Published by Cambridge University Press.

Keywords

Derived categories
Exceptional collections
Tilting object

Publisher link

10.1017/fms.2020.44

Cite this

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AU - Kaplan, Daniel

AU - Kelly, Tyler L.

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AB - 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.

KW - Derived categories

KW - Exceptional collections

KW - Tilting object

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

Abstract

Bibliographical note

Keywords

Publisher link

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Cite this