Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematic areas. Grassmannians are the building blocks for skewsymmetric tensors. Although they are ubiquitous in the literature, the geometry of their secant varieties is not completely understood. In this work we determine the singular locus of the secant variety of lines to a Grassmannian Gr(k, V) using its structure as \({{\,\textrm{SL}\,}}(V)\)-variety. We solve the problems of identifiability and tangential-identifiability of points in the secant variety: as a consequence, we also determine the second Terracini locus to a Grassmannian.

割线簇是张量分解的主要主角之一，其研究涉及纯数学和应用数学领域。格拉斯曼函数是斜对称张量的构建块。尽管它们在文献中无处不在，但它们的割线品种的几何形状尚未完全被理解。在这项工作中，我们使用其结构作为\({{\,\textrm{SL}\,}}(V)\)变量来确定格拉斯曼Gr ( k ,  V )线的割线簇的奇异轨迹。我们解决了割线簇中点的可辨识性和切向可辨识性问题：因此，我们还将第二个泰拉西尼轨迹确定为格拉斯曼轨迹。