Baur–Draisma–de Graaf conjecture on secant defectivity of Grassmannians

Let $\mathbb G(r,n)$ denote the Grassmannian of $r$-planes in projective $n$-space, and let $h$ be a positive integer. A projective variety is called $h$-defective when its $h$-secant variety has dimension smaller than the expected dimension. Baur–Draisma–de Graaf's conjecture. If $r\geq 2$, then $\mathbb G(r,n)$ is not $h$-defective, with the following exceptions:

$$(r,n,h)\in\{(2,7,3),(3,8,3),(3,8,4),(2,9,4)\}.$$

The conjecture concerns the dimensions of secant varieties of Grassmannians, which are closely related to tensor-rank and skew-symmetric matrix-rank questions. The cited source proposes this as a classification of the defective cases; its resolution status is not established by the supplied text.