Detalhes bibliográficos
| Autor(a) principal: |
Medeiros, Rainelly Cunha de |
| Data de Publicação: |
2017 |
| Tipo de documento: |
Tese
|
| Idioma: |
por |
| Título da fonte: |
Biblioteca Digital de Teses e Dissertações da UFPB |
| Texto Completo: |
https://repositorio.ufpb.br/jspui/handle/tede/9318
|
Resumo: |
In thisthesis,westudycertaindegenerations/specializationsofthegenericsquare matrix overa eld k of characteristiczeroalongitsmainrelatedstructures,suchthe determinantofthematrix,theidealgeneratedbyitspartialderivatives,thepolarmap de ned bythesederivatives,theHessianmatrixandtheidealofsubmaximalminorsof the matrix.Thedegenerationtypesofthegenericsquarematrixconsideredhereare: (1) degenerationby\cloning"(repeating)avariable;(2)replacingasubsetofentriesby zeros, inastrategiclayout;(3)furtherdegenerationsoftheabovetypesstartingfrom certain specializationsofthegenericsquarematrix,suchasthegenericsymmetric matrix andthegenericsquareHankelmatrix.Thefocusinallthesedegenerations is intheinvariantsdescribedabove,highlightingonthehomaloidalbehaviorofthe determinantofthematrix.Forthis,weemploytoolscomingfromcommutativealgebra, with emphasisonidealtheoryandsyzygytheory. |