A reduced hypersurface with exactly n isolated singular points is Veronese-Avoiding precisely when those points are ordinary nodes in general linear position.
Saito, Quasihomogene isolierte Singularit¨ aten von Hyperfl¨ achen, Invent
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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.