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Proceedings of the London Mathematical Society 2006 93(3):570-592; doi:10.1017/S002461150601598X
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© London Mathematical Society

Frobenius Splitting of Equivariant Closures of Regular Conjugacy Classes

Jesper Funch Thomsen

Institut for Matematiske Fag, Aarhus Universitet 8000 Århus C, Denmark funch{at}imf.au.dk

Received 6 June 2005. Revision received 17 January 2006.

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 (primary), 13A35 (secondary).


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