Equation of some wonderful compactifications

Details Equation of some wonderful compactifications Equation of some wonderful compactifications

2010-03-08

arxiv.org/abs/1003.1704v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

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)-eigenspace of s.

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