{"id":57114,"date":"2018-03-09T22:44:54","date_gmt":"2018-03-09T22:44:54","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/estudio-de-la-rigidez-homologica-de-combinatorias-de-rectas\/"},"modified":"2018-03-09T22:44:54","modified_gmt":"2018-03-09T22:44:54","slug":"estudio-de-la-rigidez-homologica-de-combinatorias-de-rectas","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria-algebraica\/estudio-de-la-rigidez-homologica-de-combinatorias-de-rectas\/","title":{"rendered":"Estudio de la rigidez homol\u00f3gica de combinatorias de rectas."},"content":{"rendered":"<h2>Tesis doctoral de <strong>  Marco Buzun\u00e1riz Miguel \u00e1ngel <\/strong><\/h2>\n<p>Una configuraci\u00f3n de rectas es un conjunto finito de rectas en el plano proyectivo complejo. Se pueden abstraer sus propiedades combinatorias en el concepto de combinatorias de rectas. Una de las preguntas cl\u00e1sicas sobre estos objetos es la de hasta qu\u00e9 punto la combinatoria de una configuraci\u00f3n de rectas determina la topolog\u00eda de su encaje. A este respecto se conoc\u00edan bastantes resultados cl\u00e1sicos que mostraban invariantes topol\u00f3gicos que pod\u00edan ser calculados a partir de la informaci\u00f3n combinatoria. el primer resultado que mostraba la existencia de configuraciones combinatoriamente equivalentes con distinta topolog\u00eda data de 1994, cuando rybnikov construy\u00f3 dos realizaciones de una combinatoria cuyos grupos fundamentales son no isomorfos. Tales grupos pueden ser distinguidos salvo isomorfismo homol\u00f3gicamente trivial mediante el invariante de alexander. en esta memoria se estudian diferentes condiciones combinatorias que permiten deducir que todos los isomorfismos entre grupos fundamentales son homol\u00f3gicamente triviales. Tales combinatorias reciben el nombre de homol\u00f3gicamente r\u00edgidas. para estudiar la riorigidez homol\u00f3gica de una combinatoria, introducimos en el capitulo 3 los conceptos de clase admisible y haz combinatorio, y mostramos su equiValencia. Estos objetos, aunque son de naturaleza combinatoria, permiten extraer informaci\u00f3n geom\u00e9trica. Concretamente, describen los haces de curvas encajados en la configuraci\u00f3n. Todo isomorfismo entre grupos fundamentales permuta estos haces, lo que puede ser utilizado para acotar el grupo de tales isomorfismos. Esta acotaci\u00f3n es posible gracias a la existencia de una estructura subyaciente en el conjunto de haces combinatorios. Estudiamos esta estructura a trav\u00e9s del concepto de tri\u00e1ngulo de clases admisibles, que son temas de clases admisibles cuyos n\u00facleos se cortan de manera no gen\u00e9rica. el cap\u00edtulo 4 contiene la descripci\u00f3n y justificaci\u00f3n de un m\u00e9todo para establecer la rigidez homol<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Estudio de la rigidez homol\u00f3gica de combinatorias de rectas.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Estudio de la rigidez homol\u00f3gica de combinatorias de rectas. <\/li>\n<li><strong>Autor:<\/strong>\u00a0  Marco Buzun\u00e1riz Miguel \u00e1ngel <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Zaragoza<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 19\/02\/2007<\/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> Artal Bartolo Enrique Manuel<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Lozano im\u00edzcoz Mar\u00eda teresa <\/li>\n<li>Luis Par\u00eds (vocal)<\/li>\n<li>Francisco Santos leal (vocal)<\/li>\n<li>daniel Matei (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Marco Buzun\u00e1riz Miguel \u00e1ngel Una configuraci\u00f3n de rectas es un conjunto finito de rectas en el plano [&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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