Geometry of $B\times B$-orbit closures in equivariant embeddings

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    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.
    Original languageEnglish
    JournalAdvances in Mathematics
    Pages (from-to)626-646
    Publication statusPublished - 2007


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