Laurent polynomials in Mirror Symmetry: why and how?
Alexander Kasprzyk, Victor Przyjalkowski
TL;DR
This paper surveys the use of Laurent polynomials in mirror symmetry, focusing on constructing Landau-Ginzburg models for Fano varieties, their applications in classification, and invariant computation.
Contribution
It provides an overview of the main conjectures, problems, and methods involving Laurent polynomials in the context of mirror symmetry.
Findings
Landau-Ginzburg models can be constructed for Fano varieties
These models aid in classification problems
Invariants of Fano varieties can be computed via these models
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.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology