Fibers of Landau-Ginzburg models and rationality
Sukjoo Lee, Victor Przyjalkowski
TL;DR
This paper establishes a criterion linking the rationality of Fano threefolds to the monodromy properties of their mirror Landau-Ginzburg models, providing a new perspective in mirror symmetry and algebraic geometry.
Contribution
It introduces a novel characterization of Fano threefold rationality via monodromy unipotency in mirror Landau-Ginzburg models.
Findings
Rational Fano threefolds correspond to unipotent monodromy around reducible fibers.
Provides a mirror symmetry criterion for rationality of Fano threefolds.
Establishes a link between geometric rationality and monodromy properties in mirror models.
Abstract
In this article, we study how the rationality of a Fano threefold is reflected in its standard mirror Landau-Ginzburg model and its deformations. The main result is that a Fano threefold is rational if and only if the monodromy around every reducible fiber of its generic mirror Landau-Ginzburg model is unipotent.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology