[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-957879","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Vari\u00e9t\u00e9s toriques 2025-2026\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          6\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semester 2\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ED\u00e9tail du volume horaire\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                          \u003Cspan class=\u0022field__label h4 mt-5 \u0022\u003ECours magistraux :\u003C\/span\u003E\n                                      \u003Cspan\u003E20\u003C\/span\u003E\n                      \u003C\/div\u003E\n                                                                                        \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n            \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EPr\u00e9requis\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ELes pr\u00e9requis sont la g\u00e9om\u00e9trie alg\u00e9brique et un peu de th\u00e9orie des repr\u00e9sentations.\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003EThe prerequisites are algebraic geometry and basics of representation theory.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003ELe but de ce cours est de pr\u00e9senter la classification et l\u2019\u00e9tude des premi\u00e8re propri\u00e9t\u00e9s g\u00e9om\u00e9triques des vari\u00e9t\u00e9s toriques qui sont des vari\u00e9t\u00e9s alg\u00e9briques normales obtenues comme compactifications partielles de tores (produits de groupe multiplicatif). La classification met en correspondance les vari\u00e9t\u00e9s toriques et des objets de g\u00e9om\u00e9trie convexe. On obtient de cette mani\u00e8re un dictionnaire entre propri\u00e9t\u00e9s g\u00e9om\u00e9triques et propri\u00e9t\u00e9s de convexit\u00e9 qui permet, par exemple, une caract\u00e9risation de la lissit\u00e9, une description combinatoire du groupe de Picard et de la g\u00e9om\u00e9trie birationnelle des vari\u00e9t\u00e9s toriques. Le contenu pr\u00e9visionnel est le suivant (la fin d\u00e9pendra de l\u2019avancement du cours) : - Tores et vari\u00e9t\u00e9s toriques affines - G\u00e9om\u00e9trie convexes et classification - Description des orbites, crit\u00e8re de lissit\u00e9, crit\u00e8re de propret\u00e9 - Groupes de Picard, cohomologie - G\u00e9om\u00e9trie birationnelle.\u003C\/p\u003E\n\u003Cp\u003EThe goal of these lectures is to explain the classification of toric varieties and to give the first results on their geometric properties. Toric varieties are normal varieties obtained as partial compactifications of a torus (a product the multiplicative group of a field). The classification establishes a correspondence between toric varieties and convex geometric objects. This gives a dictionary between geometric and convex properties which in particular gives simple smoothness and properness criteria as well as combinatorial descriptions of the Picard group and birational geometry. Tentative plan of the lecture (depending on time for the last sections): - Tori and affine toric varieties - Convex geometry and classification - Orbits, smoothness and properness - Picard group and cohomology - Birational geometry.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                                        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EW. Fulton, Introduction to toric varieties. Princeton Univ Press 1993. D. Cox, J. Little, H. Schenck, Toric varieties. Amer Math Soc 2011\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Terminale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]