How can I construct a polynomial function $f : \mathbb C^n \to \mathbb C^m$ whose image is not algebraic?
I can't really get anywhere here. Any hints would be greatly appreciated. Thanks
How can I construct a polynomial function $f : \mathbb C^n \to \mathbb C^m$ whose image is not algebraic?
I can't really get anywhere here. Any hints would be greatly appreciated. Thanks
I assume that by "algebraic" you mean "closed in the Zariski topology on $\mathbf C^m$". Here's an idea then, with $n = m = 2$. Define $f(z, w) = (z, zw)$. For most $z_0$, the set $\{(z_0, w) : w \in \mathbf C\}$ maps onto itself under $f$, but there is one exception.