3 problems

Vanishing-entry conjecture. Every element of the destabilization set of $U$ arises by imposing vanishing conditions on entries of the map $M$ of the minimal free resolution of $U$.

The minimal-resolution conjecture. Under these hypotheses, every sheaf destabilized at the second-last wall in this way has the asserted Gaeta resolution and block-matrix structure…

Stable base locus decomposition conjecture. If $n$ is even, then $\operatorname{Eff}(\mathcal{A}(n))\setminus\operatorname{Mov}(\mathcal{A}(n))$ has