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arxiv: 0910.2523 · v1 · submitted 2009-10-14 · 🧮 math.AG

On mixed projective curves

classification 🧮 math.AG
keywords projectivevarietymixedalgebraicbasicbehaviorcurvesdefines
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Let $f(\bfz,\bar\bfz)$ be a mixed polar homogeneous polynomial of $n$ 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 $V$ is non-singular. We study a basic property of such a variety.

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