What is the range of the map $\mathbb{C}^m\to\mathbb{C}^m$, $$(z_1,\ldots,z_m)\mapsto (b_1,\ldots,b_m),$$ where $b_k=\prod_{j\neq k}(z_j-z_k)$ for $1\leq k\leq m$ ?
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2$\begingroup$ Why the FA tag? $\endgroup$– Yemon ChoiCommented Apr 20, 2014 at 2:53
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$\begingroup$ What do you mean by range of points in $P^{m-1}$ ? $\endgroup$– mehCommented Apr 20, 2014 at 12:42
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$\begingroup$ Same question with $\mathbb{R}^m$ seems to be interesting too. $\endgroup$– Alexandre EremenkoCommented Apr 20, 2014 at 13:06
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$\begingroup$ @AlexandreEremenko Your edit seems to have changed the meaning of the original question, which was asking explicitly about the range of the map viewed as taking values in complex projective space $\endgroup$– Yemon ChoiCommented Apr 20, 2014 at 16:25
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$\begingroup$ To the original poster: what did you mean in your original question: complex affine space or complex projective space? $\endgroup$– Yemon ChoiCommented Apr 21, 2014 at 1:08
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