9 problems

Weak rigidity conjecture. If $C$ has at least three singularities, then

Main classification conjecture. The curve $C$ is free, and its exponents determine the infinite series to which it belongs as follows:

Freeness conjecture for ${\mathcal F}{\mathcal Z}_2$. The curves $C_k\in {\mathcal F}{\mathcal Z}_2(k)$ are free divisors and

Freeness conjecture for ${\mathcal F}{\mathcal Z}_1$. The curves $C_{d,a}\in {\mathcal F}{\mathcal Z}_1(d,a)$ are free divisors and $mdr(f)=2$ for all possible values of $(d,a)$ wh…

Free-or-nearly-free conjecture. A reduced plane curve $C:f=0$ which is rational cuspidal is either free or nearly free.

Let $E\subseteq\mathbb{P}^2$ be a rational cuspidal curve, and let $(X,D)$ be a log resolution of $(\mathbb{P}^2,E)$. Write $\mathbb{C}^{**}=\mathbb{C}^1\setminus\{0,1\}$. Negativi…

Rational cuspidal freeness conjecture. (i) Any rational cuspidal curve $C$ in the plane is either free or nearly free. (ii) An irreducible plane curve $C$ which is either free or n…

Four-singular-point conjecture. Every rational cuspidal curve has at most $4$ singular points. The source presents this as an old conjecture and refers to Piontkowski for a precise…

Fernández de Bobadilla–Luengo–Melle-Hernández–Némethi conjecture. For every $j=0,dots,d-3$,