2 problems

Let $R=\mathsf{k}[X_1,\ldots,X_n]$ be a polynomial ring over a field. A graded $R$-module has a pure resolution when the nonzero graded shifts in its minimal free resolution occur…

Let $R$ be a standard graded algebra over a field $\mathsf{k}$. Let $\mathbb{B}_{\mathbb{Q}}(R)$ be the rational cone generated by Betti tables of finitely generated graded $R$-mod…