Geometry of B B-orbit closures in equivariant embeddings

Xuhua He Jesper Funch Thomsen

Algebraic Geometry mathscidoc:1912.43205

Advances in Mathematics, 216, (2), 626-646, 2007.12
Let X denote an equivariant embedding of a connected reductive group G over an algebraically closed field k. Let B denote a Borel subgroup of G and let Z denote a B B-orbit closure in X. When the characteristic of k is positive and X is projective we prove that Z is globally F-regular. As a consequence, Z is normal and CohenMacaulay for arbitrary X and arbitrary characteristics. Moreover, in characteristic zero it follows that Z has rational singularities. This extends earlier results by the second author and M. Brion.
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@inproceedings{xuhua2007geometry,
  title={Geometry of B B-orbit closures in equivariant embeddings},
  author={Xuhua He, and Jesper Funch Thomsen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112928893619765},
  booktitle={Advances in Mathematics},
  volume={216},
  number={2},
  pages={626-646},
  year={2007},
}
Xuhua He, and Jesper Funch Thomsen. Geometry of B B-orbit closures in equivariant embeddings. 2007. Vol. 216. In Advances in Mathematics. pp.626-646. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221112928893619765.
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