Fibers of Landau-Ginzburg models and rationality
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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