2 problems

Let $S=\mathbb{C}[x_1,\ldots,x_n]$ with $n\geq 3$, and let $f_j\in S_{d_j}$ be homogeneous polynomials of degrees $d_j\geq 2$ such that … is a zero-dimensional complete intersectio…

Let $(P,L)$ be a linear space with $d=\#P$, and let $A$ be its associated ring. Set $n$ and $m$ to be the minimum and maximum, respectively, size of a line in $L$. Suppose…