# Equation of some wonderful compactifications

@article{Hivert2010EquationOS,
title={Equation of some wonderful compactifications},
author={Pascal Hivert},
journal={arXiv: Algebraic Geometry},
year={2010}
}
• P. Hivert
• Published 8 March 2010
• Mathematics
• arXiv: Algebraic Geometry
De Concini and Procesi have defined the wonderful compactification of a symmetric space X=G/H with G a semisimple adjoint group and H the subgroup of fixed points of G by an involution s. It is a closed subvariety of a grassmannian of the Lie algebra L of G. In this paper, we prove that, when the rank of X is equal to the rank of G, the variety is defined by linear equations. The set of equations expresses the fact that the invariant alternate trilinear form w on L vanishes on the (-1…
1 Citations

### Hilbert squares of K3 surfaces and Debarre-Voisin varieties

• Mathematics
Journal de l’École polytechnique — Mathématiques
• 2020
The Debarre-Voisin hyperk\"ahler fourfolds are built from alternating $3$-forms on a $10$-dimensional complex vector space, which we call trivectors. They are analogous to the Beauville-Donagi

## References

SHOWING 1-9 OF 9 REFERENCES

### Complete collineations revisited

The space of complete collineations is a compactification of the space of matrices of fixed dimension and rank, whose boundary is a divisor with normal crossings. It was introduced in the 19th

### Nilpotent subspaces of maximal dimension in semi-simple Lie algebras

• Mathematics
Compositio Mathematica
• 2006
We show that a linear subspace of a reductive Lie algebra $\operatorname{\mathfrak g}$ that consists of nilpotent elements has dimension at most \$\frac{1}{2}(\dim\operatorname{\mathfrak

### Cohomology of Vector Bundles and Syzygies

1. Introduction 2. Schur functions and Schur complexes 3. Grassmannians and flag varieties 4. Bott's theorem 5. The geometric technique 6. The determinantal varieties 7. Higher rank varieties 8. The

• 1991