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

David Favero, Daniel Kaplan, Tyler Kelly

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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 which does not have a full exceptional collection consisting of line bundles. This provides a counterexample to a conjecture of Lekili and Ueda.
Original languageEnglish
Pages (from-to)1-8
JournalForum of Mathematics, Sigma
Volume8
Issue numbere56
DOIs
Publication statusPublished - 16 Nov 2020

Keywords

  • derived categories
  • exceptional collections
  • tilting object

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