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

@article{Przyjalkowski2022OnSL,
  title={On singular log Calabi-Yau compactifications of Landau-Ginzburg models},
  author={Victor Przyjalkowski},
  journal={Sbornik: Mathematics},
  year={2022},
  volume={213},
  pages={88 - 108}
}
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 . For coverings of degree greater than 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… 
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References

SHOWING 1-10 OF 65 REFERENCES

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

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

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

Weak Landau–Ginzburg models for smooth Fano threefolds

We consider Landau–Ginzburg models for smooth Fano threefolds of the principal series and prove that they can be represented by Laurent polynomials. We check that these models can be compactified to

Toric Landau–Ginzburg models

This review of the theory of toric Landau–Ginzburg models describes an effective approach to mirror symmetry for Fano varieties. It focuses mainly on the cases of dimensions and , as well as on the

Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models

In this paper we prove the smoothness of the moduli space of Landau-Ginzburg models. We formulate and prove a Tian-Todorov theorem for the deformations of Landau-Ginzburg models, develop the

Hodge numbers of Landau–Ginzburg models

On Hodge numbers of complete intersections and Landau--Ginzburg models

We prove that the Hodge number $h^{1,N-1}(X)$ of an $N$-dimensional ($N\geqslant 3$) Fano complete intersection $X$ is less by one then the number of irreducible components of the central fiber of

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
...