超曲面镜的最小对数差异

IF 1.2 2区数学 Q1 MATHEMATICS Forum of Mathematics Sigma Pub Date : 2024-02-19 DOI:10.1017/fms.2024.10

Louis Esser

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引用次数: 0

摘要

对于加权投影空间中的某些类平滑 Calabi-Yau 超曲面，Berglund-Hübsch-Krawitz（BHK）镜像对称构造给出了镜像的具体描述。我们证明，这种超曲面的环自形群商数的最小对数差异与 BHK 镜像的权重和阶数密切相关。作为应用，我们展示了具有已知最小对数差异的 klt Calabi-Yau 变体。我们猜想这些例子在每个维度上都是最优的。

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Minimal log discrepancies of hypersurface mirrors

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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来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.

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