Degenerations of classical square matrices and their determinantal structure

• Ano de defesa: 2017
• Autor(a) principal: Medeiros, Rainelly Cunha de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Matriz genérica; Matriz genérica simétrica; Matriz de Hankel; Matriz Hessiana; Determinante homaloidal; Ideal gradiente; Posto linear; Generic matrix; Generic symmetric matrix; Hankel matrix; Hessian ma- trix; Homaloidal determinant; Gradient ideal; Linear rank; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9318

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.