J. Korean Math. Soc. 2021; 58(2): 451-471
Online first article November 30, 2020 Printed March 1, 2021
https://doi.org/10.4134/JKMS.j200132
Copyright © The Korean Mathematical Society.
Young Rock Kim, Mounir Nisse
Hankuk University of Foreign Studies; Jalan Sunsuria, Bandar, Sunsuria
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 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
MSC numbers: Primary 14T05, 32A60, 53D40
Supported by: This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2015R1D1A1A01059643). This work was supported by Hankuk University of Foreign Studies Research Fund. Research of Nisse was supported in part by Xiamen University Malaysia Research Fund (Grant no. XMUMRF/ 2020-C5/IMAT/0013)
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd