On mixed projective curves
arXiv:0910.2523
Abstract
Let $f(\bfz,\bar\bfz)$ be a mixed polar homogeneous polynomial of variables $\bfz=(z_1,..., z_n)$. It defines a projective real algebraic variety $V:=\{[\bfz]\in \BC\BP^{n-1} | f(\bfz,\bar\bfz)=0 \}$ 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 is non-singular. We study a basic property of such a variety.