We find a minimal generating set for the defining ideal of the schematic intersection of the set of diagonal matrices with the closure of the conjugacy class of a nilpotent matrix indexed by a hook partition. The structure of this ideal allows us to compute its minimal free resolution and give an explicit description of the graded Betti numbers, and study its Hilbert series and regularity.
Biagioli R, Faridi S, Rosas M (2007). Resolutions of De Concini-Procesi ideals of hooks. COMMUNICATIONS IN ALGEBRA, 35, 3875-3891 [10.1080/00927870701511954].
Resolutions of De Concini-Procesi ideals of hooks
Biagioli R;
2007
Abstract
We find a minimal generating set for the defining ideal of the schematic intersection of the set of diagonal matrices with the closure of the conjugacy class of a nilpotent matrix indexed by a hook partition. The structure of this ideal allows us to compute its minimal free resolution and give an explicit description of the graded Betti numbers, and study its Hilbert series and regularity.File in questo prodotto:
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