On mixed projective curves
Mutsuo Oka · IRMA lectures in mathematics and theoretical physics · 2012
Let $f(\\mathbf{z},\\bar{\\mathbf{z}})$ be a strongly polar homogeneous polynomial of $n$ variables $\\mathbf{z} =(z_1,\\dots, z_n)$. This polynomial defines a projective real algebraic variety $V = {\\mathbf{z} \\in \\mathbf{CP}^{n-1}\\,|\\,f(\\mathbf{z},\\bar{\\mathbf{z}})=0 }$ in the projective space $\\mathbf{CP}^{n-1}$. 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.