Multiplicidade de anéis 1-dimensionais e uma aplicação ao problema de Waring

Let k be an algebraically closed eld of characteristic zero and consider the polynomial ring S = k[x1, . . . , xn] endowed with the standard grading. The Waring's problem for a form F ∈ S of degree d asks about the least integer s ≥ 1 for which there exist linear forms L1, . . . , Ls ∈ S satisf...

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Detalles Bibliográficos
Autor: Messias, Daniel Correia Lemos de
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2015
País:Brasil
Institución:Universidade Federal da Paraíba (UFPB)
Repositorio:Biblioteca Digital de Teses e Dissertações da UFPB
Idioma:portugués
OAI Identifier:oai:repositorio.ufpb.br:tede/9271
Acceso en línea:https://repositorio.ufpb.br/jspui/handle/tede/9271
Access Level:acceso abierto
Palabra clave:Problema de Waring
Posto de Waring
Multiplicidade
Monômio
Waring's problem
Waring rank
Multiplicity
Monomial
CIENCIAS EXATAS E DA TERRA::MATEMATICA
Descripción
Sumario:Let k be an algebraically closed eld of characteristic zero and consider the polynomial ring S = k[x1, . . . , xn] endowed with the standard grading. The Waring's problem for a form F ∈ S of degree d asks about the least integer s ≥ 1 for which there exist linear forms L1, . . . , Ls ∈ S satisfying F = Σs i=1 Ldi. Such integer is called Waring rank of F. In this dissertation, we present a solution to this problem { due to Carlini-Catalisano-Geramita { in the case of monomials, as an interesting application of a theorem (due to the same authors) that establishes a lower bound for the multiplicity of (standard) graded, nitely generated, reduced, 1-dimensional k-algebras.