4 problems

Regularity bound conjecture. One should have

Let $\mathbb{X}$ be a finite set of reduced points in $\mathbb{P}^{s-1}$, and suppose that $I=I(\mathbb{X})$ is a complete intersection generated by $f_1,\ldots,f_c$, where $c=s-1$…

Let $I\subset S:=K[t_1,\ldots,t_s]$ be a complete intersection graded ideal of dimension $1$, generated by forms $f_1,\ldots,f_c$ with $c=s-1$, where $d_i=\deg(f_i)$ and…

Let $S$ be the standard graded polynomial ring in the paper, and let $I\subset S$ be an unmixed radical graded ideal. Assume that every associated prime of $I$ is generated by line…