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On the Jacobian Varieties of Picard Curves: Explicit Addition Law and Algebraic Structure
Author(s) -
Sarlabous Jorge Estrada,
Barreiro Ernesto Reinaldo,
Barceló Jorge Alejandro Pieiro
Publication year - 1999
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.3212080109
Subject(s) - mathematics , jacobian matrix and determinant , variety (cybernetics) , pure mathematics , algebra over a field , interpretation (philosophy) , algebraic number , mathematical analysis , computer science , statistics , programming language
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.