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.

中文翻译：

---

关于 Landau-Ginzburg 模型的奇异对数 Calabi-Yau 紧化

我们考虑构建 Fano 品种的弱 Landau-Ginzburg 模型的对数 Calabi-Yau 紧化的过程。我们将它应用于 del Pezzo 曲面和指数射影空间的覆盖 . 对于度数大于 log Calabi-Yau 紧化是奇异的；此外，不存在光滑的射影对数 Calabi-Yau 紧致化。在所考虑的情况下，我们还证明了猜想，即无穷大纤维的分量数等于 Fano 变体的反经典系统的维数。参考书目：46 个标题。