Abstract: \font\msbm=msbm10 \def\P{\hbox{\msbm P}} \def\R{\hbox{\msbm R}} A pseudo-line of a real plane curve $C$ is a global real branch of $C(\R)$ that is not homologically trivial in $\P^2(\R)$. A geometrically integral real plane curve $C$ of degree $d$ has at most $d-2$ pseudo-lines, provided that $C$ is not a real projective line. Let $C$ be a real plane curve of degree $d$ having exactly $d-2$ pseudo-lines. Suppose that the genus of the normalization of $C$ is equal to $d-2$. We show that each pseudo-line of $C$ contains exactly $3$ inflection points. This generalizes the fact that a nonsingular real cubic has exactly $3$ real inflection points.
Keywords: real plane curve, pseudo-line, inflection point
Classification (MSC2000): 14H45, 14P99
Full text of the article: