{"id":54966,"date":"2006-06-10T00:00:00","date_gmt":"2006-06-10T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/estabilidad-en-la-grassmanniana-de-sato-aplicaciones-al-estudio-del-moduli-de-fibrados\/"},"modified":"2006-06-10T00:00:00","modified_gmt":"2006-06-10T00:00:00","slug":"estabilidad-en-la-grassmanniana-de-sato-aplicaciones-al-estudio-del-moduli-de-fibrados","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria-algebraica\/estabilidad-en-la-grassmanniana-de-sato-aplicaciones-al-estudio-del-moduli-de-fibrados\/","title":{"rendered":"Estabilidad en la grassmanniana de sato. aplicaciones al estudio del moduli de fibrados"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Ana Cristina Malheiro Casimiro <\/strong><\/h2>\n<p>El estudio del m\u00f3duli de fibrados se puede realizar, entre otras, con las siguientes dos t\u00e9cnicas: teor\u00eda geom\u00e9trica de invariantes (git) y grassmannianas infinitas. Cabe preguntarse c\u00f3mo se relacionan entre s\u00ed. Observemos que los espacios de m\u00f3duli de fibrados con trivializaci\u00f3n formal construidos a partir de la grassmanniana infinita, al cocientar por el grupo sl(r,k[[z]]), permiten recuperar los obtenidos por la git ya que pasar al cociente equivaldr\u00eda a olvidar la trivializaci\u00f3n formal con la que se dot\u00f3 al fibrado. Por ello hemos abordado el estudio de la acci\u00f3n del grupo especial lineal sl(r,k[[z]]) en la grassmanniana infinita gr(k((z))a{oplus r}) (siendo r>0 y k un cuerpo algebraicamente cerrado con caracter\u00edstica 0) con especial \u00e9nfasis en la interpretaci\u00f3n de la noci\u00f3n de estabilidad y semiestabilidad as\u00ed como la aplicaci\u00f3n de estos resultados al caso de puntos de la grassmanniana correspondientes a fibrados vectoriales v\u00eda la aplicaci\u00f3n de krichever. concretamente los resultados expuestos en la memoria son: damos una definici\u00f3n de estabilidad en la grassmanniana infinita que sea coherente con git e invariante por automorfismos de la grassmanniana; con esta noci\u00f3n construimos cocientes geom\u00e9tricos en abiertos de la grassmanniana; probamos la existencia de filtraciones de harder-narasimhan y de jord\u00e1n h\u00f3lder para puntos de aquella y finalizamos relacionando la teor\u00eda desarrollada con la teor\u00eda de estabilidad en fibrados vectoriales sobre curvas.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Estabilidad en la grassmanniana de sato. aplicaciones al estudio del moduli de fibrados<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Estabilidad en la grassmanniana de sato. aplicaciones al estudio del moduli de fibrados <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Ana Cristina Malheiro Casimiro <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Salamanca<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 06\/10\/2006<\/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>Jos\u00e9 Mar\u00eda Mu\u00f1oz Porras<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: daniel Hernandez ruiperez <\/li>\n<li>Carlos armindo Arango florentino (vocal)<\/li>\n<li>vicente Mu\u00f1oz velazquez (vocal)<\/li>\n<li>joao Luis Pimentel nunes (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Ana Cristina Malheiro Casimiro El estudio del m\u00f3duli de fibrados se puede realizar, entre otras, con las [&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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