4 problems

Generic geometric syzygy conjecture. For every $p$, the space of $p$-th linear syzygies of $C$ is spanned by scrollar syzygies.

Let $g$ denote the genus of a curve over a field of characteristic $3$. Generic Green failure conjecture. Generic Green's conjecture fails in characteristic $3$ for genera $9$ and…

Let $a$ be a positive integer, let $\overline{\mathbb{F}}$ be an algebraically closed field of characteristic $p$, and let $e=(e_1,e_2)\in\overline{\mathbb{F}}^2$ be general. Let…

Minimal Resolution Conjecture. Fix integers $g,r,d,p\geq1$ such that $g-d+r\geq0$, and assume