A geometric description of the neutral component of the Jacobian of a real plane curve having many pseudo–lines

Abstract

A pseudo–line of a real plane curve is a real branch that is not homologically trivial in ℙ2(ℝ). A real plane curve C of degree d is said to have many pseudo–lines if it has exactly d – 2 pseudo–lines and if the genus of its normalization C is equal to d – 2. Let C be such a curve. We give a planar description of the neutral component of the set of real points of the Jacobian of the normalization C of C.