3 problems

Let $A$ be an Artin Gorenstein algebra with Hilbert vector $H(A)=(1,4,7,7,4,1)$, and let the Betti tables below refer to the graded Betti tables of such algebras. Nine-table and st…

Let $A$ be an Artin Gorenstein algebra with Hilbert vector $H(A)=(1,4,4,4,4,1)$. A Betti table means the graded Betti table of a minimal free resolution of $A$. Uniqueness and stro…

Let $A$ be a codimension-$3$ Artin Gorenstein algebra, and let WLP denote the weak Lefschetz property: there exists a linear form $\ell\in A_1$ such that multiplication by $\ell$ h…