{"id":94945,"date":"2009-08-07T00:00:00","date_gmt":"2009-08-07T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/arcos-y-series-de-poincare-mota%c2%advicas-de-singularidades\/"},"modified":"2009-08-07T00:00:00","modified_gmt":"2009-08-07T00:00:00","slug":"arcos-y-series-de-poincare-mota%c2%advicas-de-singularidades","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/arcos-y-series-de-poincare-mota%c2%advicas-de-singularidades\/","title":{"rendered":"Arcos y series de poincar\u00e9 mot\u00edvicas de singularidades"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Helena Cobo Pablos <\/strong><\/h2>\n<p>Null en esta tesis estudiamos un invariante de singularidades, la serie de poincar\u00e9 mot\u00edvica geom\u00e9trica pgeom (t). Es un invariante, poco conocido a\u00fan, que estudia ciertas propiedades de finitud del espacio de arcos de una variedad. El espacio de arcos de  una variedad contiene informaci\u00f3n sobre la variedad, en particular sobre el lugar singular, como demuestran trabajos recientes de ishii o de mustata.    la serie pgeom (t) fue introducida por denef y loeser y ellos mismos demostraron que es racional . Sin embargo su prueba no es constructiva, ya que utiliza eliminaci\u00f3n de cuantificadores en conjuntos semialgebraicos o importantes resultados de integraci\u00f3n mot\u00edvica. Es por tanto interesante expresar la forma racional de la serie pgeom (t) para fa milias de singularidades. En la tesis estudiamos esta serie para variedades t\u00f3ricas y para hipersuperficies casiordinarias.       en ambos casos expresamos la forma racional de la serie en funci\u00f3n de unos ideales, ideales logar\u00edtmicos jacobianos jk, para k=1,\u00c2\u00bf,d, definidos de forma combinatoria a partir del semigrupo (caso t\u00f3rico) o de los exponentes caracter\u00edsticos (caso casiordinario). Estos ideales se definen geom\u00e9tricamente en funci\u00f3n de k-formas diferenciales.    nuestras pruebas son constr uctivas y pasan por el c\u00e1lculo de las funciones generatrices asociadas a ciertos semigrupos que, en general, no son de tipo finito. Podemos ver estos semigrupos como proyecciones lineales de puntos enteros en el interior de un cono, y probamos que di chas funciones generatrices asociadas a proyecciones lineales de puntos enteros en conos abiertos tienen forma racional.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Arcos y series de poincar\u00e9 mot\u00edvicas de singularidades<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Arcos y series de poincar\u00e9 mot\u00edvicas de singularidades <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Helena Cobo Pablos <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Complutense de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 08\/07\/2009<\/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>Pedro Daniel Gonzalez Perez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: bernard Teissier <\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Helena Cobo Pablos Null en esta tesis estudiamos un invariante de singularidades, la serie de poincar\u00e9 mot\u00edvica [&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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