2016/09/07 by Young Rock Kim, Mounir Nisse, Kim, Young Rock +1
Computer Science · Mathematics · Physics and Astronomy · #14T05 #32A60 #53D40 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1609.02181
openalex publication_date 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
First, we define phase tropical hypersurfaces in terms of a degeneration data\nof smooth complex algebraic hypersurfaces in (\ℂ^*)n. Next, we prove\nthat complex hyperplanes are diffeomorphic to their degeneration called phase\ntropical hyperplanes. More generally, using Mikhalkin's decomposition into\npairs-of-pants of smooth algebraic hypersurfaces, we show that phase tropical\nhypersurfaces with smooth tropicalization, possess naturally a smooth\ndifferentiable structure. Moreover, we prove that phase tropical hypersurfaces\npossess a natural symplectic structure.\n