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

TY - JOUR

T1 - Geometry of $B\times B$-orbit closures in equivariant embeddings

AU - He, Xuhua

AU - Thomsen, Jesper Funch

PY - 2007

Y1 - 2007

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 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.

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 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.

U2 - 10.1016/j.aim.2007.06.001

DO - 10.1016/j.aim.2007.06.001

M3 - Journal article

SN - 0001-8708

VL - 216

SP - 626

EP - 646

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -