Zariski Closed Set Notation

Is there a name or notation for a Zariski closed set in $\mathbb{C}^n$ which when intersected with $\mathbb{R}^n$ has non-trivial dimension?

For example for $n=2$, if $f(x,y) = (x^2 + 1)(x^2 + y^2 - 1)$ then is there a name for sets like $\{(x,y) \in \mathbb{C}^2:f(x,y) = 0\} \cap \mathbb{R}^2 = \{(x,y) : x^2 + y^2 = 1\}$?

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 Can you give us an example? – Matt Jul 17 '11 at 21:02 Thanks! Some $n$'s appeared. – Matt Jul 17 '11 at 21:52