2017/11/27 by Mutsuo Oka, Oka, Mutsuo
Computer Science · Mathematics · #14J17 #14N99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1711.09537
openalex publication_date 2017/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let f(\bf z,\bf z) be a strongly mixed homogeneous polynomial of 3 variables \bf z=(z1,z2,z3) of polar degree q with an isolated singularity at the origin. It defines a smooth Riemann surface C in the complex projective space \mathbb P2. The fundamental group of the complement \mathbb P2∖ C is cyclic group of order q if f is homogeneous polynomial without \bf z. We propose a conjecture that this may be even true for mixed homogeneous polynomials by giving several supporting examples.