{"id":94980,"date":"2009-08-07T00:00:00","date_gmt":"2009-08-07T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/transformadas-de-fourier-mukai-para-fibraciones-genericamente-k3-o-ela%c2%adpticas\/"},"modified":"2009-08-07T00:00:00","modified_gmt":"2009-08-07T00:00:00","slug":"transformadas-de-fourier-mukai-para-fibraciones-genericamente-k3-o-ela%c2%adpticas","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria-algebraica\/transformadas-de-fourier-mukai-para-fibraciones-genericamente-k3-o-ela%c2%adpticas\/","title":{"rendered":"Transformadas de fourier-mukai para fibraciones gen\u00e9ricamente k3 o el\u00edpticas"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Dario Sanchez Gomez <\/strong><\/h2>\n<p>El objetivo de esta tesis es estudiar haces estables y sus espacios de m\u00f3duli, usando la teor\u00eda de las transformadas de fourier-mukai, en esquemas fibrados gen\u00e9ricamente en curvas ecl\u00edpticas o en superficies k3. en el caso ecl\u00edptico, encontramos algunas transformadas de fourier-mukai, para curvas gorenstein de genero aritm\u00e9tico uno y dualizante trivial, que preservan la (semi)-estabilidad de los haces de dimensi\u00f3n pura. Usando estas transformadas definimos nuevos isomorfismos entre espacios de m\u00f3duli de haces semiestables en este tipo de curvas. As\u00ed, para rango cero los espacios de m\u00f3duli son productos sim\u00e9tricos de la curva, mientras que para rango positivo s\u00f3lo hay un n\u00famero finito de espacios no isomorfos. An\u00e1logos resultados se obtienen para los espacios de m\u00f3duli relativos de haces semiestables en una fibraci\u00f3n de genero uno arbitraria. Como caso particular estudiamos los espacios de m\u00f3duli de haces semiestables en un ciclo in de n rectas proyectivas. Mostramos que los \u00fanicos haces estables de grado cero son los haces de l\u00ednea de grado cero en cada una de las componentes irreducibles de la curva, o los haces op1 (-1) soportados en una componente irreducible. Adem\u00e1s, demostramos que la componente irreducible del espacio de m\u00f3duli que contiene a los fibrados vectoriales de rango r es isomorfa al producto sim\u00e9trico r-\u00e9simo de la curva racional con un nodo. en el caso k3, obtenemos haces estables en variedades de dimensi\u00f3n tres fibradas en superficies k3 usando una transformada de fourier-mukai. Este m\u00e9todo permite construir haces estables, y en ocasiones fibrados vectoriales estables, en t\u00e9rminos de datos espectrales de un modo similar a la construcci\u00f3n del revestimiento espectral conocida para fibraciones ecl\u00edpticas. Demostramos que dichos haces son estables respecto de ciertas polarizaciones que dependen \u00fanicamente de invariantes topol\u00f3gicos. Adem\u00e1s, cuando la variedad es calabi-yau, el m\u00f3duli de haces estables obtenido con esta t\u00e9cnica puede ser visto como una variedad fibrada gen\u00e9ricamente en variedades abelianas.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Transformadas de fourier-mukai para fibraciones gen\u00e9ricamente k3 o el\u00edpticas<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Transformadas de fourier-mukai para fibraciones gen\u00e9ricamente k3 o el\u00edpticas <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Dario Sanchez Gomez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Salamanca<\/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>Ana Cristina Lopez Martin<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Luis Narv\u00e1ez macarro <\/li>\n<li>Fernando Sancho de salas (vocal)<\/li>\n<li>claudio Bartocci (vocal)<\/li>\n<li>Juan  Carlos Naranjo del val (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Dario Sanchez Gomez El objetivo de esta tesis es estudiar haces estables y sus espacios de m\u00f3duli, [&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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