Minimal Terracini loci in projective spaces

TL;DR

This paper characterizes the conditions under which non-empty Terracini sets exist in projective spaces and provides a complete description of minimal Terracini finite sets in three-dimensional projective space for certain cases.

Contribution

It offers a new characterization of Terracini sets in projective spaces and fully describes minimal Terracini finite sets in $\

Findings

Characterization of points with non-empty Terracini sets in $\

Complete description of minimal Terracini finite sets in $\

Results for cases where the number of points is less than twice the degree of the linear system.

Abstract

We characterize the number of points for which there exist non-empty Terracini sets of points in $\mathbb{P}^n$. Then we study minimally Terracini finite sets of points in $\mathbb{P}^n$ and we obtain a complete description in the case of $\mathbb{P}^3$, when the number of points is less than twice the degree of the linear system.