2

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

deabo
  • 557

1 Answers1

2

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
  • 53,909