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Nilpotent commuting varieties of reductive Lie algebras

Alexander Premet
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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 $k$.

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Alexander Premet. 2003-02-18. Nilpotent commuting varieties of reductive Lie algebras. https://doi.org/10.1007/s00222-003-0315-6

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