Jesper Funch Thomsen

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 $X$ shares the same geometric properties.

2000 Mathematics Subject Classification: 14M17, 13A35.

E-mail:
funch@imf.au.dk