4 problems

Let $A\in{\bf Z}^{d\times n}$ be a unimodular matrix of rank $d$, and let $B$ be a Gale transform of $A$. The fan $\Gamma(B)$ is the fan associated with the Gale transform $B$. Spe…

Let $A\in{\bf Z}^{d\times n}$ be a matrix of rank $d$. The Gröbner fan of $A$ is the fan whose cones encode the reduced Gröbner bases of the toric ideal associated to $A$. Sturmfel…

Let $N$ be a numerical semigroup with associated face $F_N$, and suppose that $N$ is staircase and Kunz. When $k=3$, the four-facet conjecture. $F_N$ has at most $4$ facets. This c…

Maximal-set realization conjecture. For every set of ideals $J_1,\ldots,J_s\in\textnormal{\textsf{S}}_{p(t)}^{n}$ such that