2 problems

Let $R=K[x_0,\ldots,x_n]$ be a polynomial ring over a field $K$, let $I_{\underline{d}}=(x_0^{d_0},\ldots,x_n^{d_n})$, and let $t$ be the socle degree of $R/I_{\underline{d}}$. Ass…

Let $K$ be a field of characteristic $2$, let $d$ be a positive integer, and set … The characteristic-two conjecture. The algebra $A$ has the weak Lefschetz property if and only if…