Weak Landau--Ginzburg models for smooth Fano threefolds

Details Weak Landau--Ginzburg models for smooth Fano threefolds Weak Landau--Ginzburg models for smooth Fano threefolds

2009-02-26

arxiv.org/abs/0902.4668v2

Mathematics

Algebraic Geometry

13 pages; the paper is dedicated to the memory of my teacher V. A. Iskovskikh; some minor corrections are made; the polynomial

Scientific paper

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 prove that general elements of all the pencils we found are birational to K3 surfaces. We state most of known methods of finding Landau-Ginzburg models in terms of Laurent polynomials. We state some problems concerning Laurent polynomial representations of Landau-Ginzburg models of Fano varieties.

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