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Complete homogeneous varieties: Structure and classification
Author(s):
Carlos
Sancho de Salas
Journal:
Trans. Amer. Math. Soc.
355
(2003),
3651-3667.
MSC (2000):
Primary 14M17, 14M15, 14L30, 32M10
Posted:
March 17, 2003
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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  ). 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
Email:
sancho@gugu.usal.es
DOI:
10.1090/S0002-9947-03-03280-X
PII:
S 0002-9947(03)03280-X
Received by editor(s):
February 15, 2002
Received by editor(s) in revised form:
October 11, 2002
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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