8 problems

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

Let $g$ be the genus of a general curve over an algebraically closed field $k$. Eisenbud–Schreyer's conjecture. Generic Green's Conjecture should hold whenever … The source states…

Let $g\geq 3$, and let $\mathbf{a}$ be the sequence specifying the 2-linear strand of the minimal resolution of a canonical curve. Generic Green's conjecture. There exists a curve…

Canonical ribbon conjecture. The analogue of Green's conjecture holds for every rational ribbon. This conjecture extends the relationship between linear series and syzygies from sm…

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…

Let $C\subset \mathbb{P}^{g-1}$ be a canonically embedded curve over an algebraically closed field, with coordinate ring $S_C$ and graded Betti numbers $\beta_{i,j}(C)$. Define its…

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