Eisenbud–Koh–Stillman conjecture on determinantal presentations of secant varieties of curves

Let $C$ be a smooth projective curve of genus $g$. For line bundles $A$ and $B$ on $C$ of sufficiently large degree with respect to $g$ and $k$, set $L=A\otimes B$. The $k$-th secant variety $\Sigma_k(C,L)$ is the closure of the union of the $k$-planes spanned by $k+1$ points of the image of $C$ under $L$. The catalecticant matrix $\operatorname{Cat}(A,B)$ is the matrix of the multiplication map $H^0(C,A)\otimes H^0(C,B)\to H^0(C,L)$. Eisenbud–Koh–Stillman conjecture. The ideal $I(\Sigma_k(C,L))$ is generated by the $(k+2)\times(k+2)$-minors of $\operatorname{Cat}(A,B)$; in particular, $I(\Sigma_k(C,L))$ is determinantally presented when $\deg L$ is sufficiently large. This conjecture was subsequently verified set-theoretically by Ravi and scheme-theoretically by Ginensky, so the asserted generation statement is solved.