A natural topological manifold structure of phase tropical hypersurfaces
J. Korean Math. Soc. 2021 Vol. 58, No. 2, 451-471
https://doi.org/10.4134/JKMS.j200132
Published online November 30, 2020
Printed March 1, 2021
Young Rock Kim, Mounir Nisse
Hankuk University of Foreign Studies; Jalan Sunsuria, Bandar, Sunsuria
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 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)
Downloads: Full-text PDF   Full-text HTML

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd