{"id":83171,"date":"2018-03-10T00:07:14","date_gmt":"2018-03-10T00:07:14","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/geometria-de-las-transformaciones-birracionales-del-plano\/"},"modified":"2018-03-10T00:07:14","modified_gmt":"2018-03-10T00:07:14","slug":"geometria-de-las-transformaciones-birracionales-del-plano","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/geometria-de-las-transformaciones-birracionales-del-plano\/","title":{"rendered":"Geometria de las transformaciones birracionales del plano"},"content":{"rendered":"

Tesis doctoral de Mar\u00eda Alberich Carrami\u00f1ana <\/strong><\/h2>\n

Sea — una transformaci\u00f3n birracional del plano. Un punto base (propio o infinitamente proximo) de multiplicidad m de — es por definici\u00f3n un punto base de multiplicidad m dela red c que define —. Esta memoria presenta una exposici\u00f3n de la teor\u00eda de las transformaciones birracionales del plano, estudiando las configuraciones de los puntos base. En primer lugar, se han revisado los resultados clasicos, que solo estaban bien establecidos para el caso en que los puntos base de la transformaci\u00f3n directa e inversa son propios, y se han extendido a una transformacion arbitraria. En este sentido se generaliza el teorema de clebsch, la expresi\u00f3n del jacobiano de c, y resultados sobre curvas principales. Se caracterizan las soluciones de las ecuaciones de condici\u00f3n y las matrices cumpliendo ciertas propiedades aritmeticas que corresponden a transformaciones. Se determina, a partir del grado y las multiplicidadesen los puntos base de —, la matriz caracteristica de — y, en particular, las multiplicidades de la transformacion inversa. se estudia el comportamiento efectivo en los puntos base de las curvas principales totales, comparandolo con comportamientos virtuales determinados a partir de la caracteristica de la transformacion. Se determina el comportamiento en los puntos base de las curvas de c que no tienen el comportamiento generico. se describen las relaciones de proximidad entre los puntos base de la transformacion inversa y en particular, se caracterizan las transformaciones cuya inversa no tiene puntos base infinitamente proximos. Se determinan los invariantes de una composicion de transformaciones. Como punto final de la memoria se da una nueva demostraci\u00f3n del teorema de factorizaci\u00f3n de noether, aprovechando las tecnicas desarrolladas.<\/p>\n

 <\/p>\n

Datos acad\u00e9micos de la tesis doctoral \u00abGeometria de las transformaciones birracionales del plano<\/strong>\u00ab<\/h3>\n
    \n
  • T\u00edtulo de la tesis:<\/strong>\u00a0 Geometria de las transformaciones birracionales del plano <\/li>\n
  • Autor:<\/strong>\u00a0 Mar\u00eda Alberich Carrami\u00f1ana <\/li>\n
  • Universidad:<\/strong>\u00a0 Barcelona<\/li>\n
  • Fecha de lectura de la tesis:<\/strong>\u00a0 31\/01\/2000<\/li>\n<\/ul>\n

     <\/p>\n

    Direcci\u00f3n y tribunal<\/h3>\n
      \n
    • Director de la tesis<\/strong>\n
        \n
      • Eduard Casas Alvero<\/li>\n<\/ul>\n<\/li>\n
      • Tribunal<\/strong>\n
          \n
        • Presidente del tribunal: gerald Welters dyhdalewicz <\/li>\n
        • ignacio Luengo velasco (vocal)<\/li>\n
        • ragni Piene (vocal)<\/li>\n
        • Miguel \u00e1ngel Barja y\u00e1\u00f1ez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

           <\/p>\n","protected":false},"excerpt":{"rendered":"

          Tesis doctoral de Mar\u00eda Alberich Carrami\u00f1ana Sea — una transformaci\u00f3n birracional del plano. Un punto base (propio o infinitamente proximo) […]<\/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":[2809,951,583,7711,126],"tags":[12820,100082,5304,176409,100927,176410],"class_list":["post-83171","post","type-post","status-publish","format-standard","hentry","category-algebra","category-barcelona","category-geometria","category-geometria-proyectiva","category-matematicas","tag-eduard-casas-alvero","tag-gerald-welters-dyhdalewicz","tag-ignacio-luengo-velasco","tag-maria-alberich-carraminana","tag-miguel-angel-barja-yanez","tag-ragni-piene"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/83171","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=83171"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/83171\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=83171"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=83171"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=83171"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}