4 problems

For the $d$-uple Veronese embedding of $\mathbb P^2$, let $\beta(\mathbb P^2,b;d)$ denote its Betti table with twist parameter $b$, and let its Boij–Söderberg coefficients be the c…

Recursive-coefficient conjecture. For $\varepsilon<s<\varepsilon+c$, one has

Let $L$ be an Artinian lex-ideal in the polynomial ring $\mathbf{k}[x,y,z]$. The Boij–Söderberg decomposition of $L$ is the decomposition into pure diagrams described by Theorem 2.…

Betti-cone conjecture. The cone $\mathrm{B}_{\mathbb{Q}}(Q)$ is an $(n+1)$-dimensional cone, and its closure is defined by the following $(n+2)$ extremal rays: