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.