A NATURAL TOPOLOGICAL MANIFOLD STRUCTURE OF PHASE TROPICAL HYPERSURFACES

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 int...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 58; no. 2; pp. 451 - 471
Main Authors Kim, Young Rock, Nisse, Mounir
Format Journal Article
LanguageKorean
Published 2021
Subjects
tropical variety
phase tropical hypersurface
Polyhedral complex
(co)amoeba
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Summary: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.
Bibliography:KISTI1.1003/JNL.JAKO202109651118504
ISSN:0304-9914