Abstract
We give necessary conditions for real algebraic hypersurfaces (possibly with singularities) to contain nontrivial germs of complex hypersurfaces. Moreover, if a real hypersurface $S$ in $\mathbf{C}^2$ is defined by a real polynomial of a sufficiently general form and if $S$ contains a nontrivial analytic disk, then, using the above result, we show that $S$ must contain certain complex lines.
Citation
Nguyen Quang Dieu. "Zero sets of real polynomials containing complex varieties." Illinois J. Math. 55 (1) 69 - 76, Spring 2011. https://doi.org/10.1215/ijm/1355927027
Information