Smooth Projective Symmetric Varieties with Picard Number equal to one

Details Smooth Projective Symmetric Varieties with Picard Number equal to one Smooth Projective Symmetric Varieties with Picard Number equal to one

2007-02-12

arxiv.org/abs/math/0702340v2

Mathematics

Algebraic Geometry

23 pages; some minor errors corrected, final version. To appear on "International Journal of Mathematics"

Scientific paper

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth.

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