Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
arXiv:1102.4664 · doi:10.1016/j.jalgebra.2012.11.002
Abstract
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.
v3: minor corrections for final version
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Cited by in corpus (15)
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- Katzarkov-Kontsevich-Pantev Conjecture for Fano threefolds
- Four-dimensional Fano toric complete intersections
- String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
- Degenerations to Unobstructed Fano Stanley-Reisner Schemes
- Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians of planes
- On deformations of toric Fano varieties
- Hilbert Schemes and Toric Degenerations for Low Degree Fano Threefolds
- Nef partitions for codimension 2 weighted complete intersections
- Toric Degenerations and the Laurent polynomials related to Givental's Landau-Ginzburg models
- Projecting Fanos in the mirror
- Laurent polynomials in Mirror Symmetry: why and how?
- Seshadri constants via toric degenerations
- Modularity of Landau-Ginzburg models