## The normality of closures of conjugacy classes of matrices.(English)Zbl 0822.20045

Let $$K$$ be an algebraically closed field, $$n$$ a positive integer, $$x$$ an $$n \times n$$ matrix with entries in $$K$$, let $$C(x)$$ be the orbit of $$x$$ under the adjoint action of $$\text{GL} (n,K)$$ and let $$\overline {C(x)}$$ be the Zariski closure of $$C(x)$$. H. Kraft and C. Procesi [ibid. 53, 227-247 (1979; Zbl 0434.14026)], have proved that if $$K$$ has characteristic 0 then $$\overline {C(x)}$$ is a normal, Cohen-Macaulay variety with rational singularities. The main purpose of this paper is to prove, in arbitrary characteristic, that $$\overline {C(x)}$$ is normal.

### MSC:

 20G05 Representation theory for linear algebraic groups 14L30 Group actions on varieties or schemes (quotients) 20G15 Linear algebraic groups over arbitrary fields 14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)

Zbl 0434.14026
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### References:

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