Weierstrass points on Kummer extensions

Author(s)

Abdon, Miriam ^[1] ; Borges, Herivelto ^[2] ; Quoos, Luciane ^[3]

Affiliation

^[1] Univ Fed Fluminense, IME, Rua Mario Santos Braga S-N, BR-24020140 Niteroi, RJ - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Computaao, Av Trabalhador Sao Carlense, BR-13560970 Sao Carlos, SP - Brazil

^[3] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio De Janeiro - Brazil

• Document type: Journal article
• Source: ADVANCES IN GEOMETRY; v. 19, n. 3, p. 323-333, JUL 2019.
• Web of Science Citations: 1

Abstract

For Kummer extensions given by y(m) = f(x), we discuss conditions for an integer to be a Weierstrass gap at a place P. In the case of fully ramified places, the conditions are necessary and sufficient. As a consequence, we extend independent results of several authors. Moreover, we show that if the Kummer extension is F-q2-maximal and f(x) is an element of F-q2 {[}x] has at least two roots with the same multiplicity lambda coprime to m, then m divides 2(q + 1). Under the extra condition that either m or the multiplicity of a third root of f(x) is odd, we conclude that m divides q + 1. (AU)

• FAPESP's process: 17/04681-3 - Algebraic curves over finite fields
• Grantee: Herivelto Martins Borges Filho
• Support Opportunities: Regular Research Grants