Geometry of B×B-orbit closures in equivariant embeddings

• Autores: Xuhua He, Jesper Funch Thomsen
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 216, Nº 2, 2007, págs. 626-646
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.06.001
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• Resumen

  • Abstract 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 Cohen¿Macaulay 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