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arXiv · 2304.13823

Minimal log discrepancies of hypersurface mirrors

Louis Esser
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Abstract

For certain quasismooth Calabi-Yau hypersurfaces in weighted projective space, the Berglund-H\"{u}bsch-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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Louis Esser. 2023-04-26. Minimal log discrepancies of hypersurface mirrors. https://arxiv.org/abs/2304.13823

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