Identifiability and singular locus of secant varieties to spinor varieties

Vincenzo Galgano

Published 2023-02-10Version 1

In this work the $Spin(V)$-structure of the secant variety of lines $\sigma(\mathbb S)$ to a spinor variety $\mathbb S$ is analyzed by exhibiting its partition in orbits together with their inclusions and dimensions. The problems of identifiability and tangential-identifiability in $\sigma(\mathbb S)$ are solved via inductive arguments and via what we call Clifford apolarity. As a consequence, the singular locus $Sing(\sigma(\mathbb S))$ of the secant variety of lines is determined.