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Mat. Sb., 2017, Volume 208, Number 7, Pages 84–108 (Mi msb8838)  

This article is cited in 6 scientific papers (total in 6 papers)

Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds

V. V. Przyjalkowski

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: We prove that smooth Fano threefolds have toric Landau-Ginzburg models. More precisely, we prove that their Landau-Ginzburg models, represented as Laurent polynomials, admit compactifications to families of K3 surfaces, and we describe their fibres over infinity. We also give an explicit construction of Landau-Ginzburg models for del Pezzo surfaces and any divisors on them.
Bibliography: 40 titles.

Keywords: Fano threefolds, toric Landau-Ginzburg models, Calabi-Yau compactifications.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
The research was funded by a grant of the Russian Science Foundation (project no. 14-50-00005).


DOI: https://doi.org/10.4213/sm8838

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English version:
Sbornik: Mathematics, 2017, 208:7, 992–1013

Bibliographic databases:

Document Type: Article
UDC: 512.776
MSC: Primary 14D07, 14J30, 14J45; Secondary 14M25, 14N35
Received: 14.10.2016 and 09.03.2017

Citation: V. V. Przyjalkowski, “Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds”, Mat. Sb., 208:7 (2017), 84–108; Sb. Math., 208:7 (2017), 992–1013

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  • http://mi.mathnet.ru/eng/msb/v208/i7/p84

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Przyjalkowski, C. Shramov, “Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians of planes”, Bull. Korean Math. Soc., 54:5 (2017), 1527–1575  crossref  mathscinet  isi  scopus
    2. V. V. Przyjalkowski, “On the Calabi–Yau Compactifications of Toric Landau–Ginzburg Models for Fano Complete Intersections”, Math. Notes, 103:1 (2018), 104–110  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. Lunts, V. Przyjalkowski, “Landau-Ginzburg Hodge numbers for mirrors of del Pezzo surfaces”, Adv. Math., 329 (2018), 189–216  crossref  mathscinet  zmath  isi  scopus
    4. A. B. Zheglov, “Surprising examples of nonrational smooth spectral surfaces”, Sb. Math., 209:8 (2018), 1131–1154  mathnet  crossref  crossref  adsnasa  isi  elib
    5. Vik. S. Kulikov, “On divisors of small canonical degree on Godeaux surfaces”, Sb. Math., 209:8 (2018), 1155–1163  mathnet  crossref  crossref  adsnasa  isi  elib
    6. V. V. Przyjalkowski, “Toric Landau–Ginzburg models”, Russian Math. Surveys, 73:6 (2018), 1033–1118  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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