{"id":33018,"date":"2018-03-09T09:29:56","date_gmt":"2018-03-09T09:29:56","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/hilbert-function-combinatorial-and-homological-aspects\/"},"modified":"2018-03-09T09:29:56","modified_gmt":"2018-03-09T09:29:56","slug":"hilbert-function-combinatorial-and-homological-aspects","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/hilbert-function-combinatorial-and-homological-aspects\/","title":{"rendered":"Hilbert function: combinatorial and homological aspects."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Cristina Blancafort Andreu <\/strong><\/h2>\n<p>Sea r un \u00e1lgebra standard a coeficientes en un anillo artiniano, y sea m un r-m\u00f3dulo graduado finitamente generado. En la memoria se estudia la funci\u00f3n de hilbert de m, h-m, dada en cada entero n por la longitud de la pieza de grado n de m. Esta funci\u00f3n viene dada para n&lt;&lt;0 por un polinomio h-m, el polinomio de hilbert de m.  en primer lugar se estudia el caso local, es decir, m es el anillo graduado asociado a una filtraci\u00f3n i- buena mientras que r es el correspondiente graduado asociado al ideal. En esta situaci\u00f3n se determina una relaci\u00f3n entre la diferencia entre los valores tomados por la funci\u00f3n y el polinomio de hilbert-samuel, y los m\u00f3dulos de cohomolog\u00eda local del \u00e1lgebra de rees extendida asociada a la filtraci\u00f3n. Previamente ha sido necesario, por tanto, un estudio de las propiedades cohomol\u00f3gicas de dichas \u00e1lgebras.  en segundo lugar se estudia el caso m=r. En esta situaci\u00f3n se caracterizan las funciones y los polinomios de hilbert, bajo la hip\u00f3tesis de que el anillo base contenga un cuerpo. Se dan algoritmos que permiten hacer efectivos los teoremas de caracterizaci\u00f3n.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Hilbert function: combinatorial and homological aspects.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Hilbert function: combinatorial and homological aspects. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Cristina Blancafort Andreu <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 18\/07\/1997<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Joan Elias Garcia<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: eduard Casas alvero <\/li>\n<li>enrique Nart vi\u00f1als (vocal)<\/li>\n<li>Jorge n Herzog (vocal)<\/li>\n<li>Antonio Garcia rodicio (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Cristina Blancafort Andreu Sea r un \u00e1lgebra standard a coeficientes en un anillo artiniano, y sea m [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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