Landau-Ginzburg模型的奇异对数Calabi-Yau紧化

Pub Date : 2021-02-02 DOI:10.1070/SM9510

V. Przyjalkowski

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引用次数: 4

摘要

我们考虑了构建Fano品种弱Landau-Ginzburg模型的log Calabi-Yau紧化过程。我们将其应用于del Pezzo曲面和指数投影空间的覆盖。对于大于对数次的覆盖物，Calabi-Yau紧化是奇异的;此外，不存在光滑射影对数Calabi-Yau紧化。在考虑的情况下，我们还证明了在无穷远处纤维的组分数等于法诺变种的反正则系统的维数的猜想。参考书目:46篇。

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On singular log Calabi-Yau compactifications of Landau-Ginzburg models

We consider the procedure that constructs log Calabi-Yau compactifications of weak Landau-Ginzburg models of Fano varieties. We apply it to del Pezzo surfaces and coverings of projective spaces of index . For coverings of degree greater than the log Calabi-Yau compactification is singular; moreover, no smooth projective log Calabi-Yau compactification exists. We also prove, in the cases under consideration, the conjecture that the number of components of the fibre over infinity is equal to the dimension of an anticanonical system of the Fano variety. Bibliography: 46 titles.

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