Sobre o teorema de Max Noether para curvas singulares

• Autor(a) principal: Edson Martins Gagliardi
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/38510
• topic: Max Noether; Curvas integrais; Quase Gorenstein; Sistema linear; Curvas singulares; Ideal fracionário; Ideal canônico; Semi grupo de valores; Morfismo projetivo; Modelo canônico; Maximal com condutor fixo; Gorenstein; Nearly Gorenstein; Kunz; Matemática - Teses.; Curvas algébricas - Teses.; Curvas integrais - Teses.; Teorema de Noether - Teses.

Max Noether's Theorem states that if $ \ww $ is the dualizing bundle of a non-singular, non-hyperelliptic projective curve, then the natural morphisms $ \text{Sym}^nH^0 (\omega) \to H^0( \omega^n) $ are surjectives for all $ n \geq 1 $. The result has been extended to Gorenstein curves by many different authors in different ways. More recently, it has been proven for curves with projectively normal canonical models and curves whose non-Gorenstein points are at most biramified. Based on these works, we approach the general case and extend the result to integral curves. We also connect the problem with the local structures of Commutative Algebra and derive different characterizations of non-hyperellipticity.