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

@article{Przyjalkowski2022OnSL, title={On singular log Calabi-Yau compactifications of Landau-Ginzburg models}, author={Victor Przyjalkowski}, journal={Sbornik: Mathematics}, year={2022}, volume={213}, pages={88 - 108} }

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…

## One Citation

### Laurent polynomials in Mirror Symmetry: why and how?

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We survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau–Ginzburg…

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