Zeroes of a holomorphic map $f:\mathbb{C}^n\to \mathbb{C}$ for $n\geq 2$ Why can the zeros of a holomorphic map $f:\mathbb{C}^n\to \mathbb{C}$ with $n\geq 2$ have no isolated zeros (or poles if we write it as meromorphic)?
Someone says the $n$-times Cauchy Integral formula is enough, but how does it work?

Ted is of course perfectly correct. :)
Alternatively the claim follows from Hartogs' theorem, https://en.wikipedia.org/wiki/Hartogs%27_extension_theorem, whose proof may be the origin of the Cauchy integral formula hint you received.
