Nilpotent commuting varieties of reductive Lie algebras

Abstract

We prove that the nilpotent commuting variety of a reductive Lie algebra over an algebraically closed field of good characteristic is equidimensional. In characteristic zero, this confirms a conjecture of Vladimir Baranovsky. As a by-product, we obtain tat the punctual (local) Hilbert scheme parametrising the ideals of colength $n$ in $k[[X,Y]]$ is irreducible over any algebraically closed field $k$.

25 pages

References in corpus (1)

• Sub-principal homomorphisms in positive characteristic

Cited by in corpus (11)

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• Generalized Springer Theory for D-modules on a Reductive Lie Algebra
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• On the centralizer of the sum of commuting nilpotent elements
• On the commuting probability of p-elements in a finite group
• ${\mathbb{F}}_p$-expressible subalgebras and orbits of $\mathbb{E}(r,\mathfrak{g})$
• Nilpotent commuting varieties of the Witt algebra
• Commuting involutions of Lie algebras, commuting varieties, and simple Jordan algebras
• Frobenius extensions about centralizer matrix algebras
• The nilpotent variety of $W(1;n{)}_p$ is irreducible
• Commuting varieties for nilpotent radicals