{"id":41814,"date":"1999-01-01T00:00:00","date_gmt":"1999-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/contribuciones-al-estudio-de-la-geometria-enumerativa-de-las-cubicas-planas-cuspidales\/"},"modified":"1999-01-01T00:00:00","modified_gmt":"1999-01-01T00:00:00","slug":"contribuciones-al-estudio-de-la-geometria-enumerativa-de-las-cubicas-planas-cuspidales","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/contribuciones-al-estudio-de-la-geometria-enumerativa-de-las-cubicas-planas-cuspidales\/","title":{"rendered":"Contribuciones al estudio de la geometria enumerativa de las cubicas planas cuspidales."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Josep M. Miret Biosca <\/strong><\/h2>\n<p>El objetivo b\u00e1sico de esta memoria es comprender y completar, con m\u00e9todos de geometr\u00eda algebraica actual, los resultados de schubert relativos a la geometr\u00eda enumerativa de las c\u00fabicas cuspidales del plano. Cabe se\u00f1alar que las t\u00e9cnicas que desarrollamos con esta finalidad nos proporcionan resultados sobre ciertos sistemas de curvas planas de grado arbitrario que nos permiten establecer el caso de un nodo de una conjetura de diaz-harris que afirma que el grupo de picard de la variedad de severi     (de curvas de grado   con exactamente   nodos como \u00fanicas singularidades) es de torsi\u00f3n. M\u00e1s concretamente, probamos que a (vd1) es un grupo finito de orden 6(d-2)(d2-3d+1).  referente a las c\u00fabicas planas cuspidales, calculamos los n\u00fameros de intersecci\u00f3n con las condiciones caracter\u00edsticas   y   (que una curva pase por un punto y que sea tangente a una recta, respectivamente) y las condiciones de incidencia relativas al tri\u00e1ngulo singular de una c\u00fabica cuspidal irreducible: c, v, y, que la c\u00faspide xc, la inflexi\u00f3n xv, el punto de intersecci\u00f3n xy de la tangente cuspidal con la tangente de inflexi\u00f3n est\u00e9n, respectivamente, sobre una recta; w, q, z, que la tangente de inflexi\u00f3n uq, la tangente cuspidal uz que une la punta con la inflexi\u00f3n pasen, respectivamente, por un punto.  para ello, probamos que la clausura k del grafo de la aplicaci\u00f3n racional que asigna a cada c\u00fabica cuspidal irreducible su tri\u00e1ngulo singular y su c\u00fabica dual es una compactificaci\u00f3n no singular en codimensi\u00f3n 1 de la variedad u de c\u00fabicas cuspidales irreductibles (subvariedad localmente cerrada de codimensi\u00f3n 2 del espacio proyectivo p). Demostramos que la frontera k-u est\u00e1 formada por 13 componentes irreducibles de codimensi\u00f3n 1, llamadas degeneraciones de primer orden de k. La descripci\u00f3n de las 13 degeneraciones de k coinciden con la dada por schubert excepto la degeneraci\u00f3n que schubert denomin\u00f3 n1 donde el foco dob<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Contribuciones al estudio de la geometria enumerativa de las cubicas planas cuspidales.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Contribuciones al estudio de la geometria enumerativa de las cubicas planas cuspidales. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Josep M. Miret Biosca <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de catalunya<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1999<\/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>Sebasti\u00e1n Xamb\u00f3 Descamps<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: pere Pascual gainza <\/li>\n<li>raquel Mallvibarrena (vocal)<\/li>\n<li>vicen\u00ed\u00a7 Navarro aznar (vocal)<\/li>\n<li>audun Holme (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Josep M. Miret Biosca El objetivo b\u00e1sico de esta memoria es comprender y completar, con m\u00e9todos de [&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":[2809,5301,126,15596],"tags":[105650,47499,38937,105649,9616,55179],"class_list":["post-41814","post","type-post","status-publish","format-standard","hentry","category-algebra","category-geometria-algebraica","category-matematicas","category-politecnica-de-catalunya","tag-audun-holme","tag-josep-m-miret-biosca","tag-pere-pascual-gainza","tag-raquel-mallvibarrena","tag-sebastian-xambo-descamps","tag-viceni-navarro-aznar"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/41814","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=41814"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/41814\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=41814"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=41814"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=41814"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}