Journal of Algebraic Geometry

Author(s): Michel Brion
Journal: J. Algebraic Geom. 12 (2003), 605-626.
Posted: April 15, 2003
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Abstract: Let

be a projective variety, homogeneous under a linear algebraic group. We show that the diagonal of

belongs to a unique irreducible component ${\mathcal H}_X$ of the Hilbert scheme of $X\times X$ . Moreover, ${\mathcal H}_X$ is isomorphic to the ``wonderful completion'' of the connected automorphism group of

; in particular, ${\mathcal H}_X$ is non-singular. We describe explicitly the degenerations of the diagonal in $X\times X$ , that is, the points of ${\mathcal H}_X$ ; these subschemes of $X\times X$ are reduced and Cohen-Macaulay.

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Michel Brion
Affiliation: Université de Grenoble I, Département de Mathématiques, Institut Fourier, UMR 5582 du CNRS, 38402 Saint-Martin d'Hères Cedex, France
Email: Michel.Brion@ujf-grenoble.fr

PII: S 1056-3911(03)00315-1
Received by editor(s): November 10, 2000
Posted: April 15, 2003

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