2023/04/26 by Louis Esser, Esser, Louis
Mathematics · #14E30 #14J32 #14J33 (primary) #14J40 (secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematical Approximation and Integration
paper · pdf · doi:10.48550/arxiv.2304.13823
openalex publication_date 2023/04/26 · openalex created_date 2023/04/30 · openalex updated_date 2026/07/28
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.