Projecting Fanos in the mirror
arXiv:1904.02194
Abstract
In the paper "Birational geometry via moduli spaces" by I. Cheltsov, L. Katzarkov, and V. Przyjalkowski a new structure connecting toric degenerations of smooth Fano threefolds by projections was introduced; using Mirror Symmetry these connections were transferred to the side of Landau--Ginzburg models. In the paper mentioned above a nice way to connect of Picard rank one Fano threefolds was found. We apply this approach to all smooth Fano threefolds, connecting their degenerations by toric basic links. In particular, we find a lot of Gorenstein toric degenerations of smooth Fano threefolds we need. We implement mutations in the picture as well. It turns out that appropriate chosen toric degenerations of the Fanos are given by toric basic links from a few roots. We interpret the relations we found in terms of Mirror Symmetry.
arXiv comment87 pages
References in corpus (17)
- Mirror symmetry and T-duality in the complement of an anticanonical divisor
- PALP: A Package for Analyzing Lattice Polytopes with Applications to Toric Geometry
- Smoothable del Pezzo surfaces with quotient singularities
- Dual Cones and Mirror Symmetry for Generalized Calabi-Yau Manifolds
- On G-Fano threefolds
- Mirror Symmetry and Fano Manifolds
- Minkowski Polynomials and Mutations
- Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces
- Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
- Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds
- Mutations of Laurent Polynomials and Flat Families with Toric Fibers
- Landau-Ginzburg models -- old and new
- Mutations of fake weighted projective planes
- Compactifications of spaces of Landau-Ginzburg models
- Toric Degenerations and the Laurent polynomials related to Givental's Landau-Ginzburg models
- On Fano threefolds with canonical Gorenstein singularities
- Deresonating a Tate period