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| Irreducibility of the variety of commuting nilpotent matrices |
| Abstract: We give an elementary
proof of the irreducibility of the variety of commuting pairs of nXn nilpotent
matrices over an algebraically field k, when k is of characteristic zero,
or charactersitic p greater or equal n/2. This also gives a proof of the irreducibility of the local Hilbert scheme of n points on a smooth algebraic surface over k, thanks to a model of this scheme due to H. Nakajima. |