4 problems

Let $\Gamma$ be a Buchsbaum simplicial complex, and let $b_{i,j}(\Gamma)$ and $b^e_{i,j}(\Gamma)$ denote its symmetric and exterior iterated Betti numbers. Let $\Delta(\Gamma)$ and…

A vector $h=(1,h_1,\dots,h_d) \in \mathbb{Z}^{d+1}$ is the $h$-vector of a $(d-1)$-dimensional Buchsbaum complex $\Delta$ such that $\beta_k(\Delta)=0$ for $k \leq d-3$. A vector…

Gorenstein quotient conjecture. The ring $\overline{\mathbf{k}[\Delta]}$ should be Gorenstein. This is presented as a closely related, potentially weaker conjecture to the precedin…

Socle characterization conjecture. The equality