O Teorema de Abel

• Ano de defesa: 2017
• Autor(a) principal: Ayane Adelina da Silva
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Divisores; Superfícies de Riemann; Mapa de Abel-Jacobi; Matemática; Riemann, Superficies de; Determinantes (Matematica)
• Link de acesso: http://hdl.handle.net/1843/EABA-ARMJDA

The purpose of this note is to present a proof of Abel's Theorem. Considering X be a compact Riemann surface, every principal divisor in X is a zero degree divisor. Therefore, naturally arises the following question: when a zero degree divisor is a principal divisor in X? Abel's Theorem answers this question, and stablish that if D is a zero degree divisor then D is a principal divisor of X if and only if A_0(D) = 0 on the Jacobian of X, where A0 is the map of Abel-Jacobi restricted to zero degree divisors.