Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models

Mathematics – Algebraic Geometry

Scientific paper

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v2: 22 pages, 1 figure, added discussion of Picard lattices

Scientific paper

We show that every rank one smooth Fano threefold has a weak Landau-Ginzburg model coming from a toric degeneration. The fibers of these Landau-Ginzburg models can be compactified to K3 surfaces with Picard lattice of rank 19. We also show that any smooth Fano variety of arbitrary dimension which is a complete intersection of Cartier divisors in weighted projective space has a very weak Landau-Ginzburg model coming from a toric degeneration.

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