  Secant varieties are among the main protagonists in tensor decomposition,
whose study involves 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 work we determine the singular locus of the secant variety
of lines to a Grassmannian Gr(k,V) using its structure as 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.
