Geometric Monodromy around the Tropical Limit

Abstract

Let $\{V_q{\}}_q$ be a complex one-parameter family of smooth hypersurfaces in a toric variety. In this paper, we give a concrete description of the monodromy transformation of $\{V_q{\}}_q$ around $q=\infty$ in terms of tropical geometry. The main tool is the tropical localization introduced by Mikhalkin.

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• Phase tropical hypersurfaces