{"id":15914,"date":"2002-06-03T00:00:00","date_gmt":"2002-06-03T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/geometria-enumerativa-en-una-superficie-algebraica\/"},"modified":"2002-06-03T00:00:00","modified_gmt":"2002-06-03T00:00:00","slug":"geometria-enumerativa-en-una-superficie-algebraica","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/geometria-enumerativa-en-una-superficie-algebraica\/","title":{"rendered":"Geometr\u00eda enumerativa en una superficie algebraica"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Carlos Hermoso Ortiz <\/strong><\/h2>\n<p>La memoria de tesis doctoral proporciona bases de los espacios de homolog\u00eda racional del esquema de hilbert de puntos en superficies algebraicas arbitrarias, permitiendo realizar c\u00e1lculo expl\u00edcitos en superficies con la t\u00e9cnica de geometr\u00eda enumerativa del esquema de hilbert de puntos.  se realiza una construcci\u00f3n explic\u00edta de dos tipos de bases; una descrita por subesquemas reducidos y otra descrita por subesquemas no reducidos.  para demostrar que los candidatos que se proponen constituyentes bases, se emplea la misma t\u00e9cnica que utiliza mallavibarrena para el c\u00e1lculo de bases de la homolog\u00eda del esquema de hilbert de 4 puntos: se demuestra que los candidatos a base intersecan con una matriz triangular de entradas no nulas en la diagonal y se comprueba que dichos candidatos verifican la cardinalidad requirida para las bases en los trabajos de g\u00ed\u00b6ttsche.  la segunda parte de la memoria establece una geometr\u00eda de tri\u00e1ngulos de schubert en superficies algebraicas arbitrarias, trasladando a superficies la t\u00e9cnica de geometr\u00eda enumerativa de los tri\u00e1ngulos de schubert.  para ello se define una variedad de tri\u00e1ngulos de schubert como la explosi\u00f3n sobre la diagonal de la segunda potencia cartesiana de la proyectivizaci\u00f3n del fibrado tangentes, y se calcula la cohomolog\u00eda racional de esta variedad.  la t\u00e9cnica para el c\u00e1lculo de bases es distinta del teorema de bialynichi-birula y se basa en los generadores y relaciones del anillo y en las matrices de intersecci\u00f3n de los elementos de dimensi\u00f3n complementaria.  se comprueba la validez de la geometr\u00eda construida aplic\u00e1ndola a la enumeraci\u00f3n de dobles contactos: se generalizan y se demuestran en superficies arbitrarias la f\u00f3rmula de zeuthen-schubert y las dos conjeturas de schubert sobre dobles contactos.  para el c\u00e1lculo de los dobles contactos se expresan las clases de las curvas y las de la familias de curvas como combinaciones lineales de las clases b\u00e1sicas d<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Geometr\u00eda enumerativa en una superficie algebraica<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Geometr\u00eda enumerativa en una superficie algebraica <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Carlos Hermoso Ortiz <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Complutense de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 06\/03\/2002<\/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>Ignacio Sols Lucia<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Mallavibarrena Martinez de castro raquel <\/li>\n<li>barbara Fantechi (vocal)<\/li>\n<li>roberto Mu\u00f1oz izquierdo (vocal)<\/li>\n<li>patrick Le barz (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Carlos Hermoso Ortiz La memoria de tesis doctoral proporciona bases de los espacios de homolog\u00eda racional del [&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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