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On the irreducibility of commuting varieties of nilpotent matrices

✍ Scribed by Roberta Basili

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
321 KB
Volume
268
Category
Article
ISSN
0021-8693

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✦ Synopsis

Given an n Γ— n nilpotent matrix over an algebraically closed field K, we prove some properties of the set of all the n Γ— n 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 n Γ— n nilpotent matrices over K such that [A, B] = 0 if either char K = 0 or char K 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 if either char K = 0 or char K n/2.

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