Automorphisms, Root Systems, and Compactifications of Homogeneous Varieties

Let X=G/H be a homogeneous spherical variety and A=N_G(H)/H its automorphism group. It is known that there is an equivariant compactification with exactly one closed orbit if and only if A is finite. In that case there is one which dominates all others: The standard (or wonderful) embedding X'. The purpose of the paper is to prove Brion's conjecture: If A is trivial then X' is smooth.

Appeared in: Journal of the American Mathematical Society 9 (1996) 153-174

Available files:

DVI-file (needs the symbol font lams3)
Postscript file
Pdf-file
Original article (American Mathematical Society)

Back to index

Last updated: October 26, 2000