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

@article{Przyjalkowski2013OnHN, title={On Hodge numbers of complete intersections and Landau--Ginzburg models}, author={Victor Przyjalkowski and Constantin Shramov}, journal={arXiv: Algebraic Geometry}, year={2013} }

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 (any) Calabi--Yau compactification of Givental's Landau--Ginzburg model for $X$.

## 25 Citations

### Fibers over infinity of Landau–Ginzburg models

- MathematicsCommunications in Number Theory and Physics
- 2022

We conjecture that the number of components of the fiber over infinity of Landau--Ginzburg model for a smooth Fano variety $X$ equals the dimension of the anticanonical system of $X$. We verify this…

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

- Mathematics
- 2021

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…

### LAURENT PHENOMENON FOR LANDAU-GINZBURG MODELS OF HIGH INDEX COMPLETE INTERSECTIONS IN GRASSMANNIANS

- Mathematics
- 2015

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…

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

- Mathematics
- 2017

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…

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

- Mathematics
- 2014

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…

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

- MathematicsSbornik: Mathematics
- 2022

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…

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

- Mathematics
- 2016

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…

### Toric Landau–Ginzburg models

- MathematicsRussian Mathematical Surveys
- 2018

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…

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