How can I prove that the set $\{(z, w) \in \mathbb{C}^2; |z|+|w| = 1 \}$ is not algebraic? I just need a hint. Thanks
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Hint: complex algebraic sets have even topological dimension. The set provided Has odd dimension since it is codimension $1$ in a $4$ dimensional space.
In fact it's not even real algebraic.
orangeskid
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