The ring of sections of a complete symmetric variety

Details The ring of sections of a complete symmetric variety The ring of sections of a complete symmetric variety

2002-04-30

arxiv.org/abs/math/0204354v1

Mathematics

Algebraic Geometry

15 pages, Latex

Scientific paper

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 semi-simple 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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