# Weak Landau-Ginzburg models for smooth Fano threefolds

@article{Przyjalkowski2009WeakLM, title={Weak Landau-Ginzburg models for smooth Fano threefolds}, author={Victor Przyjalkowski}, journal={arXiv: Algebraic Geometry}, year={2009} }

The paper is joined with arXiv:0911.5428 and improved.
We prove that Landau-Ginzburg models for all 17 smooth Fano threefolds with Picard rank 1 can be represented as Laurent polynomials in 3 variables exhibiting them case by case. We check that these Landau-Ginzburg models can be compactified to open Calabi-Yau varieties. In the spirit of L. Katzarkov's program we prove that numbers of irreducible components of the central fibers of compactifications of these pencils are dimensions of…

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## 47 Citations

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For each smooth Fano threefold $X$ with Picard number 1 we consider a weak Landau--Ginzburg model, that is a fibration over $\mathbb C^1$ given by a certain Laurent polynomial. In the spirit of L.…

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We consider the procedure that constructs log Calabi–Yau compactifications of weak Landau–Ginzburg models of Fano varieties. We apply it for del Pezzo surfaces and coverings of projective spaces of…

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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…

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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…

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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…

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