Abstract
We study two quite different types of Terracini loci for the order d-Veronese embedding of an n-dimensional projective space: the minimal one and the primitive one (defined in this paper). The main result is that if n=4, d≥19 and x≤2d, no subset with x points is a minimal Terracini set. We give examples that show that the result is sharp. We raise several open questions.
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