Geometry of BxB-orbit closures in equivariant embeddings

TY - UNPB

T1 - Geometry of BxB-orbit closures in equivariant embeddings

AU - He, X.

AU - Thomsen, Jesper Funch

PY - 2005

Y1 - 2005

N2 - 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 BxB-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.

AB - 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 BxB-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.

M3 - Working paper

BT - Geometry of BxB-orbit closures in equivariant embeddings

ER -