Minimal log discrepancies of hypersurface mirrors

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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
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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