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http://dx.doi.org/10.4134/JKMS.j200132

A NATURAL TOPOLOGICAL MANIFOLD STRUCTURE OF PHASE TROPICAL HYPERSURFACES  

Kim, Young Rock (Major in Mathematics Education Graduate School of Education Hankuk University of Foreign Studies)
Nisse, Mounir (Department of Mathematics Xiamen University Malaysia)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.2, 2021 , pp. 451-471 More about this Journal
Abstract
First, we define phase tropical hypersurfaces in terms of a degeneration data of smooth complex algebraic hypersurfaces in (ℂ∗)n. Next, we prove that complex hyperplanes are homeomorphic to their degeneration called phase tropical hyperplanes. More generally, using Mikhalkin's decomposition into pairs-of-pants of smooth algebraic hypersurfaces, we show that a phase tropical hypersurface with smooth tropicalization is naturally a topological manifold. Moreover, we prove that a phase tropical hypersurface is naturally homeomorphic to a symplectic manifold.
Keywords
Polyhedral complex; tropical variety; (co)amoeba; phase tropical hypersurface;
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