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

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

2008-03-05

arxiv.org/abs/0803.0722v2

Mathematics

Algebraic Geometry

Latex, 11 pages

Scientific paper

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.

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