Laurent polynomials in Mirror Symmetry: why and how?
arXiv:2112.15339 · doi:10.22199/issn.0717-6279-5279
Abstract
We survey the approach to mirror symmetry via Laurent polynomials, outlining some of the main conjectures, problems, and questions related to the subject. We discuss: how to construct Landau--Ginzburg models for Fano varieties; how to apply them to classification problems; and how to compute invariants of Fano varieties via Landau--Ginzburg models.
arXiv comment19 pages
References in corpus (21)
- Mirror symmetry and T-duality in the complement of an anticanonical divisor
- Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves
- Equivariant Gromov - Witten Invariants
- Smoothable del Pezzo surfaces with quotient singularities
- Minkowski Polynomials and Mutations
- Computing periods of rational integrals
- Quantum Periods for 3-Dimensional Fano Manifolds
- Mirror Symmetry and the Classification of Orbifold del Pezzo Surfaces
- Toric Degenerations of Fano Threefolds Giving Weak Landau-Ginzburg Models
- Mutations of Laurent Polynomials and Flat Families with Toric Fibers
- Landau-Ginzburg models -- old and new
- Mutations of fake weighted projective planes
- Laurent Inversion
- Katzarkov-Kontsevich-Pantev Conjecture for Fano threefolds
- Four-dimensional Fano toric complete intersections
- Hodge-Tate conditions for Landau-Ginzburg models
- Laurent phenomenon for Landau-Ginzburg models of complete intersections in Grassmannians of planes
- Anticanonical system of Fano fivefolds
- Rigidity properties of Fano varieties
- Projecting Fanos in the mirror
- Fibers over infinity of Landau-Ginzburg models