{"id":86363,"date":"2018-03-10T00:10:54","date_gmt":"2018-03-10T00:10:54","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/quasi-ordinary-singularities-via-toric-geometry\/"},"modified":"2018-03-10T00:10:54","modified_gmt":"2018-03-10T00:10:54","slug":"quasi-ordinary-singularities-via-toric-geometry","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/quasi-ordinary-singularities-via-toric-geometry\/","title":{"rendered":"Quasi-ordinary singularities via toric geometry"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Pedro Daniel Gonzalez Perez <\/strong><\/h2>\n<p>En esta memoria se estudian las singularidades casi-ordinarias de variedades anal\u00edticas complejas, por medio de t\u00e9cnicas de al geometr\u00eda t\u00f3rica, principalmente en el caso de g\u00e9rmenes de hipersuperficies.  las singularidades casi-ordinarias generalizan las singularidades de curvas planas. Si s es un germen irreducible de singularidad casi-ordinaria de hipersuperficie de dimensi\u00f3n de, el teorema de jung abhyankar garantiza la existencia de una parametrizaci\u00f3nde s mediante una serie de potencias compleja en indeterminadas con exponentes fraccionarios. En esta parametrizaci\u00f3n se distinguen un n\u00famero finito g de t\u00e9rminos monomiales cuyos exponentes son  vectores denominados exponentes caracter\u00edsticos. Estos exponentes determinan buena parte de la geometr\u00eda y topolog\u00eda del germen s por ejemplo el lugar singular (lipman) y el tipo topol\u00f3gico (gau).  en la memoria, a esta prametrizaci\u00f3n se le asocian d+g generadores de un semigrupo de rango d libre de torsion. Se prueba que el anillo graduado asociado a una filtraci\u00f3n del \u00e1lgebra anal\u00edtica de s con \u00edndices en el conjunto de poliedros de newton es igual al \u00e1lgebra del semigrupo con coeficientes complejos con la filtraci\u00f3n inducida. En esta relaci\u00f3n intervienen las ra\u00edces aproximadas que estudian abhyankar y moh en el caso d=1. Se demuestra que el semigrupo es independiente de la prametrizaci\u00f3n (no as\u00ed los generadores asociados), y que adem\u00e1s termina y es determinado por el tipo topol\u00f3gico de s. La aportaci\u00f3n principal de la memoria responde a una pregunta de lipman: se trata de dos m\u00e9todos de resoluci\u00f3n sumergida de singularidades de s que se construyen mediante morfismos toroidales o t\u00f3ricos que dependen s\u00f3lo del tipo topol\u00f3gico. El primer m\u00e9todo obtiene la resoluci\u00f3n como composici\u00f3n de g morfismos que preservan el car\u00e1cter casi-ordinario de la transformada estricta mientras reducen el n\u00famero de exponentes caracter\u00edsticos. El segundo m\u00e9tdo generaliza resu<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Quasi-ordinary singularities via toric geometry<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Quasi-ordinary singularities via toric geometry <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Pedro Daniel Gonzalez Perez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 La laguna<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 15\/09\/2000<\/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>Bernard Teissier<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: monique Lejeune-jalabert <\/li>\n<li>Fernando Perez gonzalez (vocal)<\/li>\n<li>ignacio Luengo velasco (vocal)<\/li>\n<li>Antonio Campillo l\u00f3pez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Pedro Daniel Gonzalez Perez En esta memoria se estudian las singularidades casi-ordinarias de variedades anal\u00edticas complejas, por [&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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