On mixed projective curves

2009/10/14 by Mutsuo Oka, Oka, Mutsuo
Mathematics · #14J17 #14N99 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Tensor decomposition and applications #math.AG #msc:14J17 #msc:14N99

paper · pdf · doi:10.48550/arxiv.0910.2523

arxiv created 2009/10/14 · openalex publication_date 2009/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(\bfz,\bfz) be a mixed polar homogeneous polynomial of n variables \bfz=(z₁,..., z_n). It defines a projective real algebraic variety V:=\[\bfz]∈ \BC\BP^n-1 | f(\bfz,\bfz)=0 \ in the projective space \BC\BP^n-1. The behavior is different from that of the projective hypersurface. The topology is not uniquely determined by the degree of the variety even if V is non-singular. We study a basic property of such a variety.

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