Reduções em Família e Multiplicidades Mistas

• Ano de defesa: 2009
• Autor(a) principal: Sarria, Luis Alberto Alba
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraí­ba; BR; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Redução em família; Multiplicidade; Polinômios de Hilbert; Elementos superficiais; Joint reduction; Multiplicity; Hilbert s polynomials; Superficial elements; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/7361

Let (R,m) be a Noetherian local ring. Mixed multiplicities of finitely many m-primary ideals were first defined by J. Risler and B. Teissier in [Teissier] and they proved that these could be described as the usual Hilbert-Samuel multiplicity of the ideal generated by an appropriated superficial sequence. This result was later generalized by D. Rees in [Rees], who first introduced the notion of joint reduction for a family of ideals and proved that the mixed multiplicities of a family of m-primary ideals could be described as the Hilbert-Samuel multiplicity of the ideal generated by a suitable joint reduction. This theorem is known as Rees mixed multiplicity theorem and it is a crucial result in the theory of mixed multiplicities for m-primary ideals. The converse of Rees theorem was given by I. Swanson in her Ph. D. thesis (see [Swanson]). In this work, we give a detailed proof of all of the above mentioned results.