Journal of Lie Theory

no. 2
Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras
Journal of Lie Theory, Volume 26 (2016) no. 2, pp. 497-533
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.
DOI: 10.5802/jolt.899
Classification: 14C05, 14L30, 14L24, 17B08, 15A27
Keywords: Hilbert scheme, Commuting variety, GIT, parabolic algebra, nilpotent orbit 
@article{JOLT_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},
     doi = {10.5802/jolt.899},
     zbl = {1350.14006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.899/}
}
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%A L. Evain
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M. Bulois; L. Evain. Nested Punctual Hilbert Schemes and Commuting Varieties of Parabolic Subalgebras. Journal of Lie Theory, Volume 26 (2016) no. 2, pp. 497-533. doi: 10.5802/jolt.899

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