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arXiv · 2302.05295

Identifiability and singular locus of secant varieties to spinor varieties

Vincenzo Galgano
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Abstract

In this work we analyze the $Spin(V)$-structure of the secant variety of lines $\sigma_{2}(\mathbb{S})$ to a Spinor variety $\mathbb{S}$ minimally embedded in its spin representation. In particular, we determine the poset of the $Spin(V)$-orbits and their dimensions. We use it for solving the problems of identifiability and tangential-identifiability in $\sigma_2(\mathbb S)$, and for determining the second Terracini locus of $\mathbb{S}$. Finally, we show that the singular locus $Sing(\sigma_{2}(\mathbb{S}))$ contains the two $Spin(V)$-orbits of lowest dimensions and it lies in the tangential variety $\tau(\mathbb{S})$: we also conjecture what it set-theoretically is.

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Vincenzo Galgano. 2023-02-10. Identifiability and singular locus of secant varieties to spinor varieties. https://doi.org/10.1142/s0219199725500890

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