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arXiv · 1805.00378

Anti-commuting varieties

Xinhong Chen·Weiqiang Wang
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Abstract

We study the anti-commuting variety which consists of pairs of anti-commuting $n\times n$ matrices. We provide an explicit description of its irreducible components and their dimensions. The GIT quotient of the anti-commuting variety with respect to the conjugation action of $GL_n$ is shown to be of pure dimension $n$. We also show the semi-nilpotent anti-commuting variety (in which one matrix is required to be nilpotent) is of pure dimension $n^2$ and describe its irreducible components.

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Xinhong Chen, Weiqiang Wang. 2018-05-01. Anti-commuting varieties. https://arxiv.org/abs/1805.00378

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