Séminaire Lotharingien de Combinatoire, B92a (2025), 17 pp.
Raphaël Paegelow
Combinatorics of the Irreducible Components of
HnΓ in Type D and E
Abstract.
We give a combinatorial model (in terms of symmetric cores) of the
indexing set of the irreducible components of
HnΓ (the
Γ-fixed points of the Hilbert scheme of n points in the
plane) containing a monomial ideal, whenever Γ is a finite
subgroup of SL2(C) isomorphic to the binary dihedral
group. Moreover, we show that, if Γ is a subgroup of
SL2(C) isomorphic to the binary tetrahedral group, to the binary
octahedral group or to the binary icosahedral group, then the
Γ-fixed points of Hn which are also fixed under the
maximal diagonal torus of SL2(C) are in fact
SL2(C)-fixed
points. Finally, we prove that in this case the irreducible components
of HnΓ
containing a monomial ideal are zero-dimensional.
Received: October 30, 2024.
Revised: March 22, 2025.
Accepted: March 24, 2025.
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