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Let D be the unit disk, and $d\ge 2$. $F=(f_1,...f_d)$ is a holomorphic map over the closure of $D^d$ to $C^d$. What information can we get about the image of $\{0\}$x $D^{d-1}$ under $F$?

Hope some characterization about it. Is it locally contained in a zero variety?

e.g: $F(\{0\}$x $D)=\{(f(t),g(t)):t \in D\}$. where $f$ and $g$ are holomorphic on the closure of $D$.

iadvd
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Hansong
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  • I learned that the image of a zero variety under a holomorphic map is contained in a union of countably many zero varieties, but I can not find the reference. – Hansong Jul 28 '15 at 03:39

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