Let $\Omega$ be a domain in $\mathbb{C}^{m}$ and $f_{1},\ldots,f_{k}:\Omega\mapsto\mathbb{C}$ are holomorphic functions. Assume that the common zero set, $Z(f_{1},\ldots,f_{k})$ is a submanifold in $\mathbb{C}^{m}$. Then is it true that codim$Z(f_{1},\ldots,f_{k})\leq k?$
2026-03-25 01:31:13.1774402273
Maximum co-dimension of a submanifold given by finitely many holomorphic functions
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