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On the Jacobian Varieties of Picard Curves: Explicit Addition Law and Algebraic Structure

✍ Scribed by Jorge Estrada Sarlabous; Ernesto Reinaldo Barreiro; Jorge Alejandro Pieiro Barceló

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
869 KB
Volume
208
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

In this paper a system of coordinates for the effective divisors on the Jacobian Variety of a Picard curve is presented. These coordinates possess a nice geometric interpretation and provide us with an unifying environment to obtain an explicit structure of algebraic variety on the Jacobian as well as an efficient algorithm for the addition of divisors.

📜 SIMILAR VOLUMES

On the JACOBIan Varieties of PICARD Curv
On the JACOBIan Varieties of PICARD Curves Defined over Fields of Characteristic p < 0
✍ J. Estrada-Sarlabous 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 554 KB

In this paper we confine ourselves to the study of the JAcoBran variety J(C) of a PICARD curve C defined over a field K of characteristic p > 0, with the aim to obtain explicit conditions under which the JACOBIan variety is ordinary or supersingular, in terms of the HASSE-WITT matrix of the PICARD c