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arXiv · 2102.01388

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

Victor Przyjalkowski
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Abstract

We consider the procedure that constructs log Calabi-Yau compactifications of weak Landau-Ginzburg models of Fano varieties. We apply it for del Pezzo surfaces and coverings of projective spaces of index one. For the coverings of degree greater then 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 saying that the number of components of the fiber over infinity %and of finite fibers is equal to the dimension of an anticanonical system of the Fano variety.

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Victor Przyjalkowski. 2021-02-02. On singular log Calabi-Yau compactifications of Landau-Ginzburg models. https://arxiv.org/abs/2102.01388

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