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A geometric description of the neutral component of the Jacobian of a real plane curve having many pseudo–lines
Author(s) -
Fichou G.,
Huisman J.
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310057
Subject(s) - normalization (sociology) , jacobian matrix and determinant , mathematics , planar , plane curve , plane (geometry) , complex plane , line (geometry) , mathematical analysis , pure mathematics , geometry , computer science , computer graphics (images) , sociology , anthropology
A pseudo–line of a real plane curve is a real branch that is not homologically trivial in ℙ 2 (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 C̃ 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 C̃ of C .