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

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.

Keywords

• Terracini locus
• double points
• Veronese embedding
• four-dimensional projective space
• primitive Terracini locus
• minimal Terracini locus