4 problems

Neumann–Wahl conjecture. Some cusps do not have a Galois cover by a complete intersection.

Golénia–Moroianu's conjecture. The latter condition on non-vanishing of the Betti numbers cannot be taken for granted.

Let $k_{\max}(d)$ be the maximal number of ordinary cusps of a plane curve of degree $d$. Langer's conjecture. … This conjecture asserts that the coefficient of $d^2$ in the known…

Dimension-dependence conjecture. The answer to whether such manifolds are locally rigid is different in dimension $4$ than in higher dimensions.