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arXiv · 1609.02181

Geometry and a natural symplectic structure of phase tropical hypersurfaces

Young Rock Kim·Mounir Nisse
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Abstract

First, we define phase tropical hypersurfaces in terms of a degeneration data of smooth complex algebraic hypersurfaces in $(\mathbb{C}^*)^n$. Next, we prove that complex hyperplanes are diffeomorphic to their degeneration called phase tropical hyperplanes. More generally, using Mikhalkin's decomposition into pairs-of-pants of smooth algebraic hypersurfaces, we show that phase tropical hypersurfaces with smooth tropicalization, possess naturally a smooth differentiable structure. Moreover, we prove that phase tropical hypersurfaces possess a natural symplectic structure.

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Young Rock Kim, Mounir Nisse. 2016-09-07. Geometry and a natural symplectic structure of phase tropical hypersurfaces. https://arxiv.org/abs/1609.02181

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