Minimal log discrepancies of hypersurface mirrors

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Abstract

For certain quasismooth Calabi-Yau hypersurfaces in weighted projective space, the Berglund-HÜbsch-Krawitz (BHK) mirror symmetry construction gives a concrete description of the mirror. We prove that the minimal log discrepancy of the quotient of such a hypersurface by its toric automorphism group is closely related to the weights and degree of the BHK mirror. As an application, we exhibit klt Calabi-Yau varieties with the smallest known minimal log discrepancy. We conjecture that these examples are optimal in every dimension.

Original languageEnglish (US)
Article numbere23
JournalForum of Mathematics, Sigma
Volume12
DOIs
StatePublished - Feb 19 2024

All Science Journal Classification (ASJC) codes

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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