Geodesic
Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras
Journal of Lie theory, Tome 26 (2016) no. 2, pp. 497-533
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

It is known that the variety parametrizing pairs of commuting nilpotent matrices is irreducible and that this provides a proof of the irreducibility of the punctual Hilbert scheme in the plane. We extend this link to the nilpotent commuting variety of some parabolic subalgebras of Mn(K) and to the punctual nested Hilbert scheme. By this method, we obtain a lower bound on the dimension of these moduli spaces. We characterize the cases where they are irreducible. In some reducible cases, we describe the irreducible components and their dimensions.
Classification : 14C05, 14L30, 14L24, 17B08, 15A27
Mots-clés : Hilbert scheme, Commuting variety, GIT, parabolic algebra, nilpotent orbit 
@article{JLT_2016_26_2_JLT_2016_26_2_a6,
     author = {M. Bulois and L. Evain},
     title = {Nested {Punctual} {Hilbert} {Schemes} and {Commuting} {Varieties} of {Parabolic} {Subalgebras}},
     journal = {Journal of Lie theory},
     pages = {497--533},
     year = {2016},
     volume = {26},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2016_26_2_JLT_2016_26_2_a6/}
}
TY  - JOUR
AU  - M. Bulois
AU  - L. Evain
TI  - Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras
JO  - Journal of Lie theory
PY  - 2016
SP  - 497
EP  - 533
VL  - 26
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JLT_2016_26_2_JLT_2016_26_2_a6/
ID  - JLT_2016_26_2_JLT_2016_26_2_a6
ER  - 
%0 Journal Article
%A M. Bulois
%A L. Evain
%T Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras
%J Journal of Lie theory
%D 2016
%P 497-533
%V 26
%N 2
%U http://geodesic.mathdoc.fr/item/JLT_2016_26_2_JLT_2016_26_2_a6/
%F JLT_2016_26_2_JLT_2016_26_2_a6
M. Bulois; L. Evain. Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras. Journal of Lie theory, Tome 26 (2016) no. 2, pp. 497-533. http://geodesic.mathdoc.fr/item/JLT_2016_26_2_JLT_2016_26_2_a6/