2003/01/20 by R. Basili, Roberta Basili, Basili, R.
Computer Science · Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Coding theory and cryptography #Commutative Algebra (math.AC) #FOS: Mathematics #Matrix Theory and Algorithms #math.AC #math.AG
paper · pdf · doi:10.48550/arxiv.math/0301215
LaTex, 27 pages, to appear in J. Algebra
arxiv created 2003/01/20 · openalex publication_date 2003/01/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.