Geodesic
Minimal log discrepancies of hypersurface mirrors
Forum of Mathematics, Sigma, Tome 12 (2024)

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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. 
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     author = {Louis Esser},
     title = {Minimal log discrepancies of hypersurface mirrors},
     journal = {Forum of Mathematics, Sigma},
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     doi = {10.1017/fms.2024.10},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.10/}
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Louis Esser. Minimal log discrepancies of hypersurface mirrors. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.10

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