2 problems

Conjecture. Every standard graded Artinian Gorenstein algebra of embedding dimension three over a field of characteristic zero has the weak Lefschetz property.

Let $\mathbbm{k}$ be any field, let $\varSigma$ be a $(d-1)$-dimensional pseudomanifold over $\mathbbm{k}$, and let $\mathbbm{k}[\varSigma]$ be its associated graded commutative fa…