English

On mixed projective curves

Algebraic Geometry 2009-10-15 v1

Abstract

Let f(\bfz,\bfzˉ)f(\bfz,\bar\bfz) be a mixed polar homogeneous polynomial of nn variables \bfz=(z1,...,zn)\bfz=(z_1,..., z_n). It defines a projective real algebraic variety V:={[\bfz]\BC\BPn1f(\bfz,\bfzˉ)=0}V:=\{[\bfz]\in \BC\BP^{n-1} | f(\bfz,\bar\bfz)=0 \} in the projective space \BC\BPn1\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 VV is non-singular. We study a basic property of such a variety.

Keywords

Cite

@article{arxiv.0910.2523,
  title  = {On mixed projective curves},
  author = {Mutsuo Oka},
  journal= {arXiv preprint arXiv:0910.2523},
  year   = {2009}
}
R2 v1 2026-06-21T13:58:00.475Z