We study the ring of sections A(X) of a complete symmetric variety X, that is of the wonderful completion of G/H where G is an adjoint semisimple group and H is the fixed subgroup for an involutorial automorphism of G. We find generators for Pic(X), we generalize the PRV conjecture to complete symmetric varieties and construct a standard monomial theory for A(X) that is compatible with G orbit closures in X. This gives a degeneration result and the rational singularityness for A(X).

The ring of section of a complete symmetric variety

Chirivi' Rocco;
2003

Abstract

We study the ring of sections A(X) of a complete symmetric variety X, that is of the wonderful completion of G/H where G is an adjoint semisimple group and H is the fixed subgroup for an involutorial automorphism of G. We find generators for Pic(X), we generalize the PRV conjecture to complete symmetric varieties and construct a standard monomial theory for A(X) that is compatible with G orbit closures in X. This gives a degeneration result and the rational singularityness for A(X).
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/467690
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