Frobenius splitting of equivariant closures of regular conjugacy classes
by Jesper Funch Thomsen
Preprints
Number 6 (March 2005)
Let G denote a connected semisimple and simply connected algebraic group over an algebraically closed field k of positive characteristic and let g denote a regular element of G. Let X denote any equivariant embedding of G. We prove that the closure of the conjugacy class of g within X is normal and Cohen-Macaulay. Moreover, when X is smooth we prove that this closure is a local complete intersection. As a consequence, the closure of the unipotent variety within X share the same geometric properties.