Weak Landau-Ginzburg models for smooth Fano threefolds

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