Transformation Groups

, Volume 4, Issue 2, pp 273-300

First online:

Compactification of symmetric varieties

  • C. De ConciniAffiliated withDipartimento di Matematica, Università di Roma “La Sapienza”
  • , T. A. SpringerAffiliated withMathematisch Instituut, Universiteit Utrecht

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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.