Let $Z$ be a closed set in a quasi projective variety $X$.

**My question is**

what can we say about $Z$ if $\dim Z=0?$

I know $\dim Z=0$ implies all irreducible components of $Z$ is zero-dimensional.

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Let $Z$ be a closed set in a quasi projective variety $X$.

**My question is**

what can we say about $Z$ if $\dim Z=0?$

I know $\dim Z=0$ implies all irreducible components of $Z$ is zero-dimensional.

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