# Exemples de schémas de Hilbert invariants et de schémas quot invariants

Abstract : In a first part, we consider a complex connected reductive group G, and we classify the simple modules whose cone of primitive vectors admits a nontrivial G-invariant deformation. We relate this classification to that of simple Jordan algebras, and to that (due to Akhiezer) of smooth projective varieties whose orbits under the action of a connected affine algebraic group are a divisor and its complementary. Our main tool is the invariant Hilbert scheme of Alexeev-Brion; we determine the first examples of it. We also determine the infinitesimal deformations (non necessarily G-invariant) of the cones of primitive vectors; they turn out to be trivial for most simple modules. In a second part, we build the invariant Quot scheme'', and we determine a class of examples of it in the case where the ambient space is a cone of primitive vectors.
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Cited literature [15 references]

https://tel.archives-ouvertes.fr/tel-00010901
Contributor : Martine Barbelenet <>
Submitted on : Tuesday, November 8, 2005 - 10:56:48 AM
Last modification on : Wednesday, November 4, 2020 - 2:16:11 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:33:16 PM

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• HAL Id : tel-00010901, version 1

### Citation

Sébastien Jansou. Exemples de schémas de Hilbert invariants et de schémas quot invariants. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00010901⟩

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