Mathematics > Algebraic Geometry
[Submitted on 1 May 2018 (v1), last revised 27 Apr 2019 (this version, v2)]
Title:Anti-commuting varieties
View PDFAbstract: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.
Submission history
From: Weiqiang Wang [view email][v1] Tue, 1 May 2018 15:02:27 UTC (27 KB)
[v2] Sat, 27 Apr 2019 16:13:33 UTC (26 KB)
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