Nondefectivity of GL-invariant secant varieties

Abstract

We study the dimensions of higher-order secants of varieties, which are closed under the action of the general linear group. We show that if these varieties live in a Schur functor, then the secant dimensions behave as expected, up to a few potential exceptions. As applications, we derive the generic identifiability of many secants to Grassmannian varieties and to Gaussian moment varieties, and we give bounds for the generic rank with respect to these. In particular, we partially resolve a conjecture due to Baur-Draisma-deGraaf. Joint work with Alex Casarotti.

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