Fibers of Landau-Ginzburg models and rationality
arXiv:2510.21222
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.
29 pages