Hodge numbers of Fano threefolds via Landau--Ginzburg models

Abstract

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. Katzarkov's program we prove that the number of irreducible components of the central fiber of its compactification is $h^{1,2}(X)+1$. In particular, it does not depend on the compactification. The question of dependence on the model is open; however we produce examples of different weak Landau--Ginzburg models for the same variety with the same number of components of the central fiber.

The paper is now a part of the paper arXiv:0902.4668

Cited by in corpus (2)

• Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
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