Equation of some wonderful compactifications

@article{Hivert2010EquationOS,
  title={Equation of some wonderful compactifications},
  author={Pascal Hivert},
  journal={arXiv: Algebraic Geometry},
  year={2010}
}
  • P. Hivert
  • Published 8 March 2010
  • Mathematics
  • arXiv: Algebraic Geometry
De Concini and Procesi have defined the wonderful compactification of a symmetric space X=G/H with G a semisimple adjoint group and H the subgroup of fixed points of G by an involution s. It is a closed subvariety of a grassmannian of the Lie algebra L of G. In this paper, we prove that, when the rank of X is equal to the rank of G, the variety is defined by linear equations. The set of equations expresses the fact that the invariant alternate trilinear form w on L vanishes on the (-1… 
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