Abstract
The symmetric varieties considered in this paper are the quotientsG/H, whereG is an adjoint semi-simple group over a fieldk of characteristic ≠ 2, andH is the fixed point group of an involutorial automorphism ofG which is defined overk. In the casek=C, De Concini and Procesi (1983) constructed a “wonderful” compactification ofG/H. We prove the existence of such a compactification for arbitraryk. We also prove cohomology vanishing results for line bundles on the compactification.
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Dedicated to the memory of C. Chevalley
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De Concini, C., Springer, T.A. Compactification of symmetric varieties. Transformation Groups 4, 273–300 (1999). https://doi.org/10.1007/BF01237359
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DOI: https://doi.org/10.1007/BF01237359