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

@article{Przyjalkowski2016CalabiYauCO,
  title={Calabi-Yau compactifications of toric Landau-Ginzburg models for smooth Fano threefolds},
  author={Victor Przyjalkowski},
  journal={Sbornik: Mathematics},
  year={2016},
  volume={208},
  pages={992 - 1013}
}
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. 

On the Calabi–Yau Compactifications of Toric Landau–Ginzburg Models for Fano Complete Intersections

It is well known that Givental’s toric Landau–Ginzburg models for Fano complete intersections admit Calabi–Yau compactifications. We give an alternative proof of this fact. As a consequence of this

On Calabi-Yau compactifications of Landau-Ginzburg models for coverings of projective spaces

We suggest the procedure that constructs a log Calabi–Yau compactification of weak Landau–Ginzburg model of a Fano variety. We apply the suggestion for del Pezzo surfaces and coverings of projective

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

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Fibers over infinity of Landau–Ginzburg models

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Toric Landau–Ginzburg models

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Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians

In 1997 Batyrev, Ciocan-Fontanine, Kim, and van Straten suggested a construction of Landau–Ginzburg models for Fano complete intersections in Grassmannians similar to Givental’s construction for

Hodge numbers of Landau–Ginzburg models

Projecting Fanos in the mirror

In the paper "Birational geometry via moduli spaces" by I. Cheltsov, L. Katzarkov, and V. Przyjalkowski a new structure connecting toric degenerations of smooth Fano threefolds by projections was

Calabi–Yau threefolds fibred by high rank lattice polarized K3 surfaces

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It is well known that Givental’s toric Landau–Ginzburg models for Fano complete intersections admit Calabi–Yau compactifications. We give an alternative proof of this fact. As a consequence of this

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