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

  title={On singular log Calabi-Yau compactifications of Landau-Ginzburg models},
  author={Victor Przyjalkowski},
  journal={Sbornik: Mathematics},
  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… 
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