4 problems

Generic dimension and non-smoothability conjecture. For generic $L_r^n$, equality holds in the stated bounds for $\dim T^1_l$ when $l>0$ and for $\dim T^1_{-1}$, with some exceptio…

Let $C$ be a Gorenstein monomial curve of Stöhr–Torres type. Stöhr–Torres non-smoothability conjecture. The curve $C$ is not smoothable. The conjecture is motivated by the example…

Smoothability conjecture. $Z$ is smoothable for all $m,n\in\mathbb{N}$.

Rigidity conjecture. There exist no rigid fat points, no rigid reduced curve singularities, and no rigid normal surface singularities.