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.
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