5 problems

Let $I$ be a grade $c$ perfect ideal in a local Noetherian ring $R$. Let $d$ denote the deviation of $I$ and $t$ the minimal number of generators of $\operatorname{Ext}^c(R/I,R)$.…

Let $w^{(1)}$ be the top coordinate associated with the higher structure maps of a grade-three perfect ideal having Dynkin Betti numbers. Genericity conjecture. For a general choic…

Let $S$ be a local $\mathbb{C}$-algebra and suppose that … resolves $S/I$ for some perfect ideal $I$. Genericity conjecture for codimension three. There exists a homomorphism…

Let $\mathfrak{I}\subseteq Q$ be a grade $3$ perfect ideal of class $\mathbf{G}$ that is not Gorenstein. Write $m_{\mathfrak{I}}$ for its first deviation, $n_{\mathfrak{I}}$ for it…

Let $m$ be the first deviation and $n$ the type of a codimension $3$ Cohen–Macaulay local ring. Consider rings of class $\mathbf{B}$, $\mathbf{H}$, or $\mathbf{T}$, subject to the…