Singularities of the 2nd secant varieties to Grassmannians

Secant varieties are among the main protagonists in tensor decomposition, whose research covers both pure and applied mathematical 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 talk we discuss the singular locus of the secant variety of lines to a Grassmannian Gr(k,V) using its structure as SL(V)-variety, also solving the problems of identifiability and tangential-identifiability of points in the secant variety. This is based on a joint work with Reynaldo Staffolani.