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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| 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 |
| 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. |
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