On mixed plane curves of degree 1

2010/05/10 by Oka, Mutsuo
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1005.1449

Abstract

Let f(\bfz,\bfz) be a mixed strongly polar homogeneous polynomial of 3 variables \bfz=(z₁,z₂, z₃). It defines a Riemann surface V:=\[\bfz]∈ \BP² | f(\bfz,\bfz)=0 \ in the complex projective space \BP². We will show that for an arbitrary given g≥ 0, there exists a mixed polar homogeneous polynomial with polar degree 1 which defines a projective surface of genus g. For the construction, we introduce a new type of weighted homogeneous polynomials which we call \em polar weighted homogeneous polynomials of twisted join type.

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