On mixed projective curves

  • Mutsuo Oka

    Tokyo University of Science, Japan
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Let f(z,zˉ)f(\mathbf{z},\bar{\mathbf{z}}) be a strongly polar homogeneous polynomial of nn variables z=(z1,,zn)\mathbf{z} =(z_1,\dots, z_n). This polynomial defines a projective real algebraic variety V={[z]CPn1f(z,zˉ)=0}V = \{[\mathbf{z}] \in \mathbf{CP}^{n-1}\,|\,f(\mathbf{z},\bar{\mathbf{z}})=0 \} in the projective space CPn1\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 VV is non-singular. We study a basic property of such a variety.