We introduce and study properties of the Terracini locus of projective varieties X, which is the locus of finite sets \(S \subset X\) such that 2S fails to impose independent conditions to a linear system L. Terracini loci are relevant in the study of interpolation problems over double points in special position, but they also enter naturally in the study of special loci contained in secant varieties to projective varieties.

We find some criteria which exclude that a set S belongs to the Terracini locus. Furthermore, in the case where X is a Veronese variety, we bound the dimension of the Terracini locus and we determine examples in which the locus has codimension 1 in the symmetric product of X.

我们介绍并研究了射影变种X的Terracini轨迹的属性，该特性是有限集\（S \ subset X \）的轨迹，使得2 S无法对线性系统L施加独立条件。Terracini基因座与特殊位置双点插值问题的研究有关，但它们也自然地适用于割线变种至投影变种中包含的特殊基因座的研究。

我们发现一些排除集合S属于Terracini轨迹的标准。此外，在X是Veronese变体的情况下，我们限制Terracini基因座的维数，并确定其中X的对称乘积中基因座维数为1的示例。