6 problems

Let an extremal ray of the cone of Betti tables be given, and consider its integral points. Eisenbud–Fløystad–Weyman conjecture. Every sufficiently large integral point on an extre…

Let $S$ be the polynomial ring in the paper, and let $d=(d_0,\dots,d_{n+1})\in\mathbb{Z}^{n+2}$ be a strictly increasing degree sequence. A pure resolution of type $d$ is a minimal…

Small pure resolution conjecture. For any pair of partitions $\lambda^{(0)}\subsetneq\lambda^{(1)}$, such a small pure resolution exists, equivariantly for both $\mathbf{GL}(V)$ an…

Fix a vector bundle $\mathcal{E}$ on $\mathbb{P}^n$. Let $f$ be the root sequence corresponding to the first step of the Boij–Söderberg decomposition of $\mathcal{E}$, and let…

Let ${\bf d}$ be a degree sequence, and let $\pi({\bf d})$ denote the smallest integer diagram on the ray $t\pi({\bf d})$ for $t>0$. Such integer diagrams are $m\pi({\bf d})$ for…

Eisenbud–Weyman conjecture. Any sufficiently large integral point along an extremal ray is the Betti table of a module.