Complete homogeneous varieties: Structure and classification |
| |
Authors: | Carlos Sancho de Salas |
| |
Affiliation: | Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 3-4, C.P. 37008, España |
| |
Abstract: | Homogeneous varieties are those whose group of automorphisms acts transitively on them. In this paper we prove that any complete homogeneous variety splits in a unique way as a product of an abelian variety and a parabolic variety. This is obtained by proving a rigidity theorem for the parabolic subgroups of a linear group. Finally, using the results of Wenzel on the classification of parabolic subgroups of a linear group and the results of Demazure on the automorphisms of a flag variety, we obtain the classification of the parabolic varieties (in characteristic different from ). This, together with the moduli of abelian varieties, concludes the classification of the complete homogeneous varieties. |
| |
Keywords: | |
|
| 点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Transactions of the American Mathematical Society》下载全文 |
|