{"id":140125,"date":"2026-01-12T17:51:46","date_gmt":"2026-01-12T17:51:46","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/clasificacion-de-singularidades-de-curvas-planas-y-valoraciones-divisoriales\/"},"modified":"2026-01-12T17:51:46","modified_gmt":"2026-01-12T17:51:46","slug":"clasificacion-de-singularidades-de-curvas-planas-y-valoraciones-divisoriales","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/clasificacion-de-singularidades-de-curvas-planas-y-valoraciones-divisoriales\/","title":{"rendered":"Clasificacion de singularidades de curvas planas y valoraciones divisoriales."},"content":{"rendered":"<h2>Tesis doctoral de <strong>  Aparicio Pedre\u00f1o Jos\u00e9 Juan <\/strong><\/h2>\n<p>La tesis esta dividida en tres capitulos. El capitulo i se titula \u00abinvariantes de equisingularidad de curvas irreducibles sobre un cuerpo perfecto\u00bb y consta de tres secciones:  1.1) preliminares.  1.2) desarrollos de hamburguer-noether de curvas irreducibles planas y cuerpos de coeficientes.  1.3) sistemas completos de invariantes.  el capitulo ii se titula \u00abarboles y funciones de enriques de curvas reducidas con coeficientes en un cuerpo perfecto\u00bb y consta de cinco secciones:  2.1) grafos de enriques.  2.2) satelitismo y libertad.  2.3) funciones de enriques.  2.4) apendice i: arboles de enriques.  2.5) apendice ii: formulas de paso.  el capitulo iii se titula \u00abideales simples, valoraciones divisoriales y equisingularidad de curvas irreducibles sobre un cuerpo perfecto\u00bb y consta de dos secciones:  3.1) ideales, valoraciones y transformaciones cuadraticas.  3.2) grafos duales y funciones de enriques.  los problemas que han motivado este trabajo son:  problema 1.- Clasificacion de singularidades de curvas planas definidas sobre un cuerpo perfecto.  problema 2.- Desarrollar la teoria de las valoraciones v centradas en un anillo r local regular de dimension de krull dos que verifican: rat. Rk v + tr. Degk v = dim r.  los resultados obtenidos al abordar el problema 1, en los capitulos i y ii, asi como otros ya existentes, nos han permitido abordar el problema 2, cuando el cuerpo residual es perfecto y centrandonos en el estudio de las valoraciones divisoriales. Ponemos de manifiesto que la funcion de enriques construida por nosotros determina la estructura combinatoria de dichas valoraciones y de los objetos equivalentes que describe el teorema final de este trabajo.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Clasificacion de singularidades de curvas planas y valoraciones divisoriales.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Clasificacion de singularidades de curvas planas y valoraciones divisoriales. <\/li>\n<li><strong>Autor:<\/strong>\u00a0  Aparicio Pedre\u00f1o Jos\u00e9 Juan <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Valladolid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1992<\/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>Tom\u00e1s S\u00e1nchez Giralda<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Jos\u00e9 Manuel Aroca Hernandez Ros <\/li>\n<li>Angel Granja Baron (vocal)<\/li>\n<li> Gomez Pardo Jos\u00e9 Luis (vocal)<\/li>\n<li>Mark Spivakovsky (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Aparicio Pedre\u00f1o Jos\u00e9 Juan La tesis esta dividida en tres capitulos. El capitulo i se titula \u00abinvariantes [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2809,5301,126,12451],"tags":[12794,254685,2812,12587,158482,2813],"class_list":["post-140125","post","type-post","status-publish","format-standard","hentry","category-algebra","category-geometria-algebraica","category-matematicas","category-valladolid","tag-angel-granja-baron","tag-aparicio-pedreno-jose-juan","tag-gomez-pardo-jose-luis","tag-jose-manuel-aroca-hernandez-ros","tag-mark-spivakovsky","tag-tomas-sanchez-giralda"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/140125","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=140125"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/140125\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=140125"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=140125"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=140125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}