Minimal and Primitive Terracini Loci of a Four-Dimensional Projective Space.

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 ≤ 2 d , 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. [ABSTRACT FROM AUTHOR]