On the irreducibility of commuting varieties of nilpotent matrices

DOI10.1016/S0021-8693(03)00388-0zbMath1032.15012arXivmath/0301215OpenAlexW1970504483MaRDI QIDQ1409743

Roberta Basili

Publication date: 22 October 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0301215

zbMATH Keywords

Hilbert schemenilpotent matrixirreducibility of the variety of matrix pairs

Mathematics Subject Classification ID

Algebraic systems of matrices (15A30)

Related Items (21)

On the maximal nilpotent orbit that intersects the centralizer of a matrix ⋮ On the nilpotent commutator of a nilpotent matrix ⋮ Enumeration of commuting pairs in Lie algebras over finite fields ⋮ Commuting nilpotent matrices and Artinian algebras. ⋮ Bound on the Jordan type of a generic nilpotent matrix commuting with a given matrix ⋮ The poset of the nilpotent commutator of a nilpotent matrix ⋮ The smallest part of the generic partition of the nilpotent commutator of a nilpotent matrix ⋮ On varieties of commuting nilpotent matrices ⋮ Nilpotent commuting varieties of reductive Lie algebras ⋮ Degree of the variety of pairs of nilpotent commuting matrices ⋮ Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit ⋮ Pairs of commuting nilpotent matrices, and Hilbert function ⋮ The commutator algebra of a nilpotent matrix and an application to the theory of commutative Artinian algebras ⋮ Injective strong commutativity preservers on \(\mathcal{T}_{\infty}(F)\) ⋮ Jordan forms for mutually annihilating nilpotent pairs ⋮ The degrees of varieties of nilpotent matrices ⋮ On the variety of almost commuting nilpotent matrices ⋮ On pairs of commuting nilpotent matrices ⋮ Conjugacy classes of commuting nilpotents ⋮ Maximal subalgebras of finite-dimensional algebras ⋮ Artinian algebras and Jordan type

Cites Work

• Description de Hilb sup(n) C{X,Y}
• On the irreducibility of varieties of commuting matrices
• Commuting varieties of Lie algebras over fields of prime characteristic
• On dominance and varieties of commuting matrices
• Pairs of Matrices With Property L. II
• Géométrie des schémas de Hilbert ponctuels
• Punctual Hilbert schemes
• On the normality of commuting varieties of symmetric matrices
• The variety of pairs of commuting nilpotent matrices is irreducible
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