## Some remarks on varieties of pairs of commuting upper triangular matrices and an interpretation of commuting varieties

Basili, Roberta
##### Description
It is known that the variety of pairs of n x n commuting upper triangular matrices isn't a complete intersection for infinitely many values of n; we show that there exists m such that this happens if and only if n > m. We also show that m < 18 and that it could be found by determining the dimension of the variety of pairs of commuting strictly upper triangular matrices. Then we define a natural map from the variety of pairs of commuting n x n matrices onto a subvariety defined by linear equations of the grassmannian of subspaces of codimension 2 of a vector space of dimension n x n.
Comment: Latex, 11 pages
##### Keywords
Mathematics - Algebraic Geometry, Mathematics - Operator Algebras, 15A30, 14L30