  We show that a large class of secant varieties is nondefective. In
particular, we positively resolve most cases of the Baur-Draisma-de Graaf
conjecture on Grassmannian secants in large dimensions. Our result improves the
known bounds on nondefectivity for various other secant varieties, including
Chow varieties, Segre-Veronese varieties and Gaussian moment varieties. We also
give bounds for identifiability and the generic ranks.
