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Group law on the neutral component of the Jacobian of a real hyperelliptic curve having many real components

✍ Scribed by Goulwen Fichou

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
129 KB
Volume
181
Category
Article
ISSN
0022-4049

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✦ Synopsis

Let C be a real algebraic curve of genus g with at least g real components B1; : : : ; Bg. We give an embedding of C into a blow up in one point of the projective plane. It allows us to describe geometrically the neutral real component Pic o (C) o of the Jacobian of C thanks to an isomorphism with the product B1 × • • • × Bg. This induces an explicit geometric description of Pic o (C) o in the projective plane, where the group law is given by intersection with curves of genus g.

📜 SIMILAR VOLUMES

A geometric description of the neutral c
A geometric description of the neutral component of the Jacobian of a real plane curve having many pseudo–lines
✍ G. Fichou; J. Huisman 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 102 KB

## Abstract 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