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On the Irreducibility of Commuting Varieties of Nilpotent Matrices | R. Basili
; | Date: |
20 Dec 2002 | Subject: | Algebraic Geometry; Commutative Algebra | math.AG math.AC | Abstract: | Given an nxn nilpotent matrix over an algebraically closed field K, we prove some properties of the set of all the nxn nilpotent matrices over K which commute with it. Then we give a proof of the irreducibility of the variety of all the pairs (A,B) of nxn nilpotent matrices over K if either char K = 0 or char K isn’t less than n/2. We get as a consequence a proof of the irreducibility of the local Hilbert scheme of n points of a smooth algebraic surface over K with the previous condition on char K. | Source: | arXiv, math.AG/0301215 | Services: | Forum | Review | PDF | Favorites |
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