6 problems

Let ${\pmb k}$ be a field of characteristic zero, let $n$ be even, and set … Suppose that $n+1$ elements of $J$ of degree $n$ have been produced. Generation conjecture. These $n+1$…

Miller–Villarreal conjectures. One always has

E8 specialization conjecture. For every such ideal $I\subset R$, there exists a ring homomorphism

Specialization conjecture. Then $I$ is a specialization of the Kustin–Miller model or of the generic model.

Let $I$ be a codimension-four Gorenstein ideal generated by $n$ elements, and let the higher structure maps associated with a self-dual resolution of $R/I$ be suitably interpreted.…

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