Abstract
Given a smooth subvariety of dimension greater than $(2/3)(r-1)$ in $\mathbb {P}\sp r$, we show that the double locus (upstairs) of its generic projection to $\mathbb {P}\sp {r-1}$ is irreducible. This implies a version of Zak's linear normality theorem.
Citation
Angelo Felice Lopez. Ziv Ran. "On the irreducibility of secant cones, and an application to linear normality." Duke Math. J. 117 (3) 389 - 401, 15 April 2003. https://doi.org/10.1215/S0012-7094-03-11731-7
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