Geodesic
Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras
Michaël Bulois1 ; Laurent Evain2
1Institut Camille Jordan, Université Jean Monnet, Maison de l'Université, 10 rue Tréfilerie, 42023 Saint-Etienne Cedex 2, France
2Dép. de Maths, Faculté des Sciences, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France
Journal of Lie Theory, Tome 26 (2016) no. 2, pp. 497-533

Voir la notice de l'article provenant de la source Heldermann Verlag

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

Michaël Bulois  1   ; Laurent Evain  2

1 Institut Camille Jordan, Université Jean Monnet, Maison de l'Université, 10 rue Tréfilerie, 42023 Saint-Etienne Cedex 2, France
2 Dép. de Maths, Faculté des Sciences, Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France 
Michaël Bulois; Laurent 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/JOLT_2016_26_2_a6/
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     author = {Micha\"el Bulois and Laurent 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/JOLT_2016_26_2_a6/}
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