A reduced hypersurface with exactly n isolated singular points is Veronese-Avoiding precisely when those points are ordinary nodes in general linear position.
Dimca, Syzygies of Jacobian ideals and defects of linear systems, Bull
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Veronese Avoiding Hypersurfaces
A reduced hypersurface with exactly n isolated singular points is Veronese-Avoiding precisely when those points are ordinary nodes in general linear position.