A natural topological manifold structure of phase tropical hypersurfaces
J. Korean Math. Soc.
Published online November 30, 2020
Young Rock Kim and Mounir Nisse
Hankuk University of Foreign Studies, Xiamen University Malaysia
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 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 phase tropical hypersurface with smooth tropicalization, is naturally a topological manifold. Moreover, we prove that phase tropical hypersurface is naturally homeomorphic to a symplectic manifold.
Keywords : Polyhedral complex, tropical variety, (co)amoeba, phase tropical hypersurface
MSC numbers : 14T05, 32A60, 53D40
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