9 problems

Let $X\rightarrow\mathbb{P}^2$ be the double plane ramified over a smooth sextic curve. A smooth $2$-polarized $K3$-surface is such a double plane equipped with its polarization of…

Degtyarev's conjecture. If $g(\SS)>0$, then $\SS$ is realized by exactly two rigid isotopy classes of irreducible sextics, one abundant and one not. If $g(\SS)=0$, then $\SS$ is re…

Degtyarev's conjecture. Up to equisingular deformation, $C$ is determined by its set of singularities and its Alexander polynomial.

Connectedness and abelianity conjecture. The space $\mathcal M_{nt}(6A_2;6)$ is connected, and the fundamental group

Torus-type conjecture. If

Let $C$ be a smooth real plane sextic of rigid isotopy type $(71)$. A bitangent of $C$ is a line tangent to $C$ at two points, and it is real when its defining line is real. Type…

Let $C$ be a smooth sextic curve in the real projective plane $\mathbb{P}^2_\mathbb{R}$. A bitangent of $C$ is a line tangent to $C$ at two points, and a bitangent is real when it…

Finiteness conjecture. If $B$ is not of torus type, then the fundamental group $\pi_1(\mathbb{P}^2\setminus B)$ is finite.

Finite fundamental group conjecture. If $B$ is not of torus type, then