Geodesic
Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds
Sbornik. Mathematics, Tome 208 (2017) no. 7, pp. 992-1013

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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
Mots-clés : Calabi-Yau compactifications. 
@article{SM_2017_208_7_a3,
     author = {V. V. Przyjalkowski},
     title = {Calabi-Yau compactifications of toric {Landau-Ginzburg} models for smooth {Fano} threefolds},
     journal = {Sbornik. Mathematics},
     pages = {992--1013},
     publisher = {mathdoc},
     volume = {208},
     number = {7},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2017_208_7_a3/}
}
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V. V. Przyjalkowski. Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds. Sbornik. Mathematics, Tome 208 (2017) no. 7, pp. 992-1013. http://geodesic.mathdoc.fr/item/SM_2017_208_7_a3/