The secant linear virtual dimension conjecture for hypersurfaces through general points

Let $X$ be the blow-up of ${\mathbb P}^n$ at $n+3$ general points, and let $D$ be a divisor on $X$ as in the source. Let $\operatorname{\sigma ldim}(D)$ denote the secant linear virtual dimension of the corresponding linear system. The secant linear virtual dimension conjecture.

$$h^0(X,\mathcal{O}_X(D))=\max\{0,\operatorname{\sigma ldim}(D)\}.$$

This is presented as a conjectural answer to the dimensionality problem for linear systems of hypersurfaces through $n+3$ general points, in connection with the Fröberg–Iarrobino conjectures.