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Geometry of B imes B-orbit closures in equivariant embeddings

Xuhua He Jesper Funch Thomsen

Algebraic Geometry mathscidoc:1912.43234

arXiv preprint math/0510088
Let X denote an equivariant embedding of a connected reductive group X over an algebraically closed field X . Let X denote a Borel subgroup of X and let X denote a X -orbit closure in X . When the characteristic of X is positive and X is projective we prove that X is globally X -regular. As a consequence, X is normal and Cohen-Macaulay for arbitrary X and arbitrary characteristics. Moreover, in characteristic zero it follows that X has rational singularities. This extends earlier results by the second author and M. Brion.
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@inproceedings{xuhuageometry,
  title={Geometry of B imes B-orbit closures in equivariant embeddings},
  author={Xuhua He, and Jesper Funch Thomsen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113105122689794},
  booktitle={arXiv preprint math/0510088},
}
Xuhua He, and Jesper Funch Thomsen. Geometry of B imes B-orbit closures in equivariant embeddings. In arXiv preprint math/0510088. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113105122689794.
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