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Transactions of the American Mathematical Society

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Complete homogeneous varieties: Structure and classification

Author: Carlos Sancho de Salas
Journal: Trans. Amer. Math. Soc. 355 (2003), 3651-3667
MSC (2000): Primary 14M17, 14M15, 14L30, 32M10
Published electronically: March 17, 2003
MathSciNet review: 1990167
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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 $2,3$). This, together with the moduli of abelian varieties, concludes the classification of the complete homogeneous varieties.

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Additional Information

Carlos Sancho de Salas
Affiliation: Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 3-4, C.P. 37008, España

Received by editor(s): February 15, 2002
Received by editor(s) in revised form: October 11, 2002
Published electronically: March 17, 2003
Additional Notes: This research was partially supported by the Spanish DGI through research project BFM2000-1315 and by the “Junta de Castilla y León” through research project SA009/01
Article copyright: © Copyright 2003 American Mathematical Society

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