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Smooth Projective Symmetric Varieties with Picard Number equal to one

Alessandro Ruzzi
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Abstract

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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Alessandro Ruzzi. 2008-09-26. Smooth Projective Symmetric Varieties with Picard Number equal to one. https://arxiv.org/abs/math/0702340

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