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Sbornik: Mathematics, 2022, Volume 213, Issue 1, Pages 88–108
DOI: https://doi.org/10.1070/SM9510 (Mi sm9510) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

V. V. Przyjalkowski

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
English version PDF (577 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM9510
Abstract: 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, Calabi-Yau compactifications, Fano varieties, coverings.
Funding agency Grant number
Russian Science Foundation 19-11-00164
This work was supported by the Russian Science Foundation under grant no. 19-11-00164.
Received: 04.09.2020 and 27.05.2021
Russian version:
Matematicheskii Sbornik, 2022, Volume 213, Number 1, Pages 95–118
DOI: https://doi.org/10.4213/sm9510
Bibliographic databases:
Document Type: Article
UDC: 512.76
MSC: 14J33
Language: English
Original paper language: Russian
Citation: V. V. Przyjalkowski, “On singular log Calabi-Yau compactifications of Landau-Ginzburg models”, Mat. Sb., 213:1 (2022), 95–118; Sb. Math., 213:1 (2022), 88–108
Citation in format AMSBIB
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