Gonalidade e o Teorema de Max Noether para Curvas Não-Gorenstein

• Ano de defesa: 2013
• Autor(a) principal: Lia Feital Fusaro Abrantes
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Modelo canônico de Rosenlicht; Curvas não-Gorenstein; Semigrupos de valores; Teorema de Max Noether; Gonalidade; Matemática
• Link de acesso: http://hdl.handle.net/1843/EABA-9AQHMH

The gonality of a curve C is the smallest integer d such that there exists a linear system of degree d and dimension 1 in C, possibly admitting non-removable base points. We show that the gonality of a non-Gorenstein curve of arithmetic genus g ranges from 2 to g and that the greatest possible gonality for a non-Gorenstein rational curve with a unique singular point coincides with the Brill-Noether's bound for non-singular curves. Furthermore, we prove some additional results on gonality for curves of arbitrary genus. Afterwards, we make a detailed analysis of all possible gonalities of non-Gorenstein curves of genus 5 in accordance with their respective canonical models. At the last part, we obtain our main result: the generalization of Max Noether's Theorem for all integral nonhyperelliptic curves. And we also compute the dimension of the vector space of r-forms vanishing on a unibranch non-Gorenstein curve.