3 problems

Let $\mathbf{k}$ be a field, let $S=\mathbf{k}[x_1,\ldots,x_n]$, and for $d\in\mathbf{N}$ let $E(d)\subseteq S$ be the unique lexsegment ideal such that … and, for some $r$,…

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.…

Let $A=B=K[X_1,\dots,X_n]$, let $\mathfrak a=(f_1,\dots,f_r)$ be generated by a homogeneous regular sequence with degrees $d_1\leq\cdots\leq d_r$, and let $R=A/\mathfrak a$. Set…