Identifiability and singular locus of secant varieties to Spinor varieties

In this work, we analyze the Formula: see text-structure of the secant variety of lines Formula: see text to a Spinor variety Formula: see text minimally embedded in its spin representation. In particular, we determine the poset of the Formula: see text-orbits and their dimensions. We use it for solving the problems of identifiability and tangential-identifiability in Formula: see text, and for determining the second Terracini locus of Formula: see text. Finally, we show that the singular locus Formula: see text contains the two Formula: see text-orbits of lowest dimensions and it lies in the tangential variety Formula: see text: we also conjecture what it set-theoretically is.