5 problems

Let $d\ge 3$, let $1\le a\le b\le d-1$ with $\operatorname{GCD}(a,b,d)=1$, and let … where $e$ is a $d$-th root of unity. Let $I:=I^d_{0,a,b}\subset R$ be the GT-system generated b…

Let $P$ be a smooth monomial Togliatti system of cubics in $k[x_0,\ldots,x_n]$, defining a projective variety of dimension $n$. The truncated-simplex system is … which has dimensio…

The minimal monomial Togliatti conjecture. Every minimal monomial Togliatti system of degree $d$ satisfies precisely one Laplace equation of order $d-1$.

Let $P$ be a smooth monomial Togliatti system of cubics, and consider the family of smooth monomial Togliatti systems of cubics obtained by the procedure described immediately befo…

Partition-generation conjecture. All smooth monomial Togliatti systems of cubics are obtained in this way.