English

Smooth Projective Symmetric Varieties with Picard Number equal to one

Algebraic Geometry 2008-09-26 v2 Representation Theory

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.

Keywords

Cite

@article{arxiv.math/0702340,
  title  = {Smooth Projective Symmetric Varieties with Picard Number equal to one},
  author = {Alessandro Ruzzi},
  journal= {arXiv preprint arXiv:math/0702340},
  year   = {2008}
}

Comments

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

R2 v1 2026-07-22T17:50:56.018Z