2 problems

Let $k[\mathbf{x}]=k[x_1,x_2,x_3]$ and $k[\mathbf{y}]=k[y_1,y_2,y_3,y_4]$. Consider the matrix $\varphi:=\varphi_{3,r}$ as in the paper's template, and let…

Let $I=(x^a,y^b)\cap (y^c,z^d)\cap (x^e,z^f)$, where … Write $A(I)$ for the symbolic Rees algebra of $I$, and let $d(A(I))$ denote its depth. Lower-bound conjecture. … This propose…