Geodesic
On singular log Calabi-Yau compactifications of Landau-Ginzburg models
Sbornik. Mathematics, Tome 213 (2022) no. 1, pp. 88-108

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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 $1$. For coverings of degree greater than $2$ 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.
Keywords: Landau-Ginzburg models, Fano varieties, coverings.
Mots-clés : Calabi-Yau compactifications 
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     title = {On singular log {Calabi-Yau} compactifications of {Landau-Ginzburg} models},
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V. V. Przyjalkowski. On singular log Calabi-Yau compactifications of Landau-Ginzburg models. Sbornik. Mathematics, Tome 213 (2022) no. 1, pp. 88-108. http://geodesic.mathdoc.fr/item/SM_2022_213_1_a3/