2000/10/23 by Michel Brion, Brion, Michel · 1 citation
Mathematics · #14C05 #14M15 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG #msc:14C05 #msc:14M15
paper · pdf · doi:10.48550/arxiv.math/0010215
LaTeX2e, 20 pages
arxiv created 2000/10/23 · openalex publication_date 2000/10/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
Let X be a projective variety, homogeneous under a linear algebraic group. We show that the diagonal of X belongs to a unique irreducible component HX of the Hilbert scheme of X× X. Moreover, HX is isomorphic to the ``wonderful completion'' of the connected automorphism group of X; in particular, HX is non-singular. We describe explicitly the degenerations of the diagonal in X× X, that is, the points of HX; these subschemes of X× X are reduced and Cohen-Macaulay.