3 problems

Let $r\ge1$, $c>2-r$, and let $\mathcal{A}$ be a homogeneous $t\times(t+c-1)$ matrix with entries of degree $a_j-b_i$. Set $A=R/I_{t-r+1}(\mathcal{A})$ and suppose…

Fix integers $r\ge1$, $c>2-r$, $t\ge2$, and $d\ge1$. Let $\mathcal{A}$ be a homogeneous $t\times(t+c-1)$ matrix with entries of degree $e$, and set $A=R/I_{t-r+1}(\mathcal{A})$. Su…

The dimension conjecture. Under these hypotheses,