On the irreducibility of commuting varieties of nilpotent matrices

By Robert A. M. Basili. 2003

56 citations recorded by the source corpus.

Abstract Given an n × n nilpotent matrix over an algebraically closed field  K , we prove some properties of the set of all the n × 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 × 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.

Subfields: Algebra and Number Theory, Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/74758125d19a58f619ed79c560be325f44f2843e

Citations in the corpus

• Nilpotent commuting varieties of reductive Lie algebras (2003, unknown): “R T ] 1 8 Fe b 20 03”