{"id":99891,"date":"2018-03-11T10:21:11","date_gmt":"2018-03-11T10:21:11","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/invariantes-de-singularidades-en-caractera%c2%adstica-positiva\/"},"modified":"2018-03-11T10:21:11","modified_gmt":"2018-03-11T10:21:11","slug":"invariantes-de-singularidades-en-caractera%c2%adstica-positiva","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/invariantes-de-singularidades-en-caractera%c2%adstica-positiva\/","title":{"rendered":"Invariantes de singularidades en caracter\u00edstica positiva."},"content":{"rendered":"

Tesis doctoral de Angelica Benito Sualdea <\/strong><\/h2>\n

Invariantes de singularidades en caracter\u00edstica positiva ang\u00e9lica benito sualdea director: orlando e. Villamayor uriburu la presente tesis doctoral aborda uno de los problemas centrales de la geometr\u00eda algebraica: el problema de resoluci\u00f3n de singularidades, es decir, dada una variedad algebraica x, decidir si existe una variedad x1 junto con un morfismo birracional y propio . en la memoria se trata el caso de caracter\u00edstica positiva (problema que sigue abierto desde principios del siglo xx), en ella se introducen nuevos invariantes de la singularidad siguiendo la l\u00ednea iniciada en [vi] y [brvi]. En la primera parte de la tesis se estudia a fondo el marco de trabajo desarrollado por villamayor en [vi], dando lugar a la demostraci\u00f3n de que cierto invariante de la singularidad (el invariante tau de hironaka) tiene un buen comportamiento con eliminaci\u00f3n, este resultado se recoge en [be]. la segunda parte de la tesis se dedica a definir y estudiar nuevos invariantes propios de la singularidad en caracter\u00edstica positiva. Las t\u00e9cnicas desarrolladas en esta memoria son la base de las ideas tratadas en [bevi1], donde se demuestra resoluci\u00f3n de singularidades si ciertas condiciones num\u00e9ricas se satisfacen (caso fuertemente monomial). Otra aplicaci\u00f3n de las ideas de la tesis y de [bevi1] se encuentra en [bevi2], donde se demuestra resoluci\u00f3n de singularidades en el caso de superficies. Los anteriores resultados se pueden generalizar a situaciones m\u00e1s generales (como resoluci\u00f3n de cualquier esquema de dimensi\u00f3n 2) usando los resultados expuestos en [bevi3]. bibliograf\u00eda: [be] a. Benito, the \u00c2\u00bf-invariant and elimination, j. Algebra, 324 (2010), 1903 – 1920. [bevi1] a. Benito, o. E. Villamayor u., Techniques for the study of singularities with applications to resolution of 2-dimensional schemes, math. Ann. 353 (2012), no. 3, 1037 – 1068. [bevi2] a. Benito, o. E. Villamayor u., Monoidal transforms and invariants of singularities in positive characteristic. Aceptado para su publicaci\u00f3n en compositio mathematica. [bevi3] a. Benito, o. E. Villamayor u., On elimination of variables in the study of singularities in positive characteristic. Preprint 2011. Disponible en: http:\/\/arxiv.Org\/abs\/1103.3462 [brvi] a. Bravo, o. E. Villamayor u., Singularities in positive characteristic, stratification and simplification of the singular locus, adv. Math., 224 (4) (2010) 1349 – 1418. [vi] o. E. Villamayor u., Hypersurface singularities in positive characteristic, adv. Math. 213 (2007), no. 2, 687 – 733.<\/p>\n

 <\/p>\n

Datos acad\u00e9micos de la tesis doctoral \u00abInvariantes de singularidades en caracter\u00edstica positiva.<\/strong>\u00ab<\/h3>\n
    \n
  • T\u00edtulo de la tesis:<\/strong>\u00a0 Invariantes de singularidades en caracter\u00edstica positiva. <\/li>\n
  • Autor:<\/strong>\u00a0 Angelica Benito Sualdea <\/li>\n
  • Universidad:<\/strong>\u00a0 Aut\u00f3noma de Madrid<\/li>\n
  • Fecha de lectura de la tesis:<\/strong>\u00a0 22\/03\/2010<\/li>\n<\/ul>\n

     <\/p>\n

    Direcci\u00f3n y tribunal<\/h3>\n
      \n
    • Director de la tesis<\/strong>\n
        \n
      • Orlando Villamayor<\/li>\n<\/ul>\n<\/li>\n
      • Tribunal<\/strong>\n
          \n
        • Presidente del tribunal: herwig Hauser <\/li>\n
        • josep Alvarez montaner (vocal)<\/li>\n
        • adolfo Quiros gracian (vocal)<\/li>\n
        • Santiago Encinas carrion (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

           <\/p>\n","protected":false},"excerpt":{"rendered":"

          Tesis doctoral de Angelica Benito Sualdea Invariantes de singularidades en caracter\u00edstica positiva ang\u00e9lica benito sualdea director: orlando e. Villamayor uriburu […]<\/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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[126],"tags":[29907,203680,137589,203682,203681,96625],"class_list":["post-99891","post","type-post","status-publish","format-standard","hentry","category-matematicas","tag-adolfo-quiros-gracian","tag-angelica-benito-sualdea","tag-herwig-hauser","tag-josep-alvarez-montaner","tag-orlando-villamayor","tag-santiago-encinas-carrion"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/99891","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=99891"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/99891\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=99891"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=99891"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=99891"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}