8 problems

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 $X$ be a ribbon of genus $g$ with reduced curve $X_{\mathrm{red}}$ of genus $\bar{g}\ge 2$, let $\delta=-\deg({\mathscr N})$, where ${\mathscr N}$ is the conormal sheaf, and le…

Let $X$ be a ribbon, let $\delta=-\deg({\mathscr N})$, and let $\bar{g}$ be the genus of $X_{\mathrm{red}}$. The large-nilradical component conjecture. If … then the only irreducib…

Let $X$ be a ribbon and let ${\mathscr F}$ be a pure sheaf on $X$ that is not a generalized vector bundle. A sheaf generizes to another sheaf if it occurs as a special fiber of a f…

Let $\mathcal{R}((a+1)^n a^m)$ be the poset of ribbons whose row lengths consist of $n$ copies of $a+1$ and $m$ copies of $a$, ordered by Schur-positivity. Unique-minimal-element c…

Let $\mathcal{R}((a+1)^n a^m)$ be the poset of ribbons whose row lengths consist of $n$ copies of $a+1$ and $m$ copies of $a$, ordered by Schur-positivity. Let $P_{R,S}$ denote the…

Let $N$ be fixed, let $\lambda\vdash N$, and consider the subposet of $\mathcal{P}_{N}$ consisting of ribbons $R$ whose row partition is $\operatorname{rows}(R)=\lambda$. For a rib…

Fix $N$ and the number of rows $l$, so that an equitable ribbon has $N-l+1$ columns, and restrict to equitable ribbons whose rows all have length at least $2$. Write…