7 problems

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

Rigidity conjecture. If $C$ has at least three singularities, then $C$ is FZ-projectively rigid and FZ-unobstructed. In particular, $C$ is $es$-rigid.

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…

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…

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