Fibers over infinity of Landau-Ginzburg models
@article{Cheltsov2020FibersOI, title={Fibers over infinity of Landau-Ginzburg models}, author={Ivan Cheltsov and Victor Przyjalkowski}, journal={arXiv: Algebraic Geometry}, year={2020} }
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 conjecture for log Calabi--Yau compactifications of toric Landau--Ginzburg models for smooth Fano threefolds, complete intersections, and some toric varieties.
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References
SHOWING 1-10 OF 19 REFERENCES
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…
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…
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…
On Hodge numbers of complete intersections and Landau--Ginzburg models
- Mathematics
- 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…
Toric degenerations of Fano threefolds giving weak Landau–Ginzburg models
- Mathematics, Physics
- 2013
Weak Landau–Ginzburg models for smooth Fano threefolds
- Mathematics
- 2009
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…
Bogomolov-Tian-Todorov theorems for Landau-Ginzburg models
- Mathematics
- 2014
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…
Katzarkov-Kontsevich-Pantev Conjecture for Fano threefolds.
- Mathematics
- 2018
We verify Katzarkov-Kontsevich-Pantev conjecture for Landau-Ginzburg models of smooth Fano threefolds.
Anticanonical divisors and curve classes on Fano manifolds
- Mathematics
- 2010
It is well known that the Hodge conjecture with rational coefficients holds for degree 2n-2 classes on complex projective n-folds. In this paper we study the more precise question if on a rationally…