Inflection Points on Real Plane Curves Having Many Pseudo-Lines
نویسنده
چکیده
A pseudo-line of a real plane curve C is a global real branch of C(R) that is not homologically trivial in P(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. MSC 2000: 14H45, 14P99
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