14 problems

Let $\widehat{P}$ be the compactification obtained from the moduli space of plane quartics by the construction described in the paper. Consider the moduli space of polarized K3 sur…

Catanese's conjecture. The technical assumption on the singular points is always satisfied.

Let $\overline{K}$ be an algebraically closed field of characteristic $p$, and let the paper's singularity-classification algorithm be denoted by Algorithm 1. Positive-characterist…

Let $p$ be a positive characteristic, and let Theorem on the correspondence between Dixmier–Ohno invariants and singularity types be denoted by the referenced theorem. Positive-cha…

Symplectic equivariance conjecture. The action of $\operatorname{Sp}(6,2)$ on $\operatorname{PGL}_3(\overline{K})$-equivalence classes of Cayley octads commutes with the map $d_K$.

Octad picture stable-reduction conjecture. The stable reduction type, including whether or not it is hyperelliptic, of any smooth plane quartic over any non-archimedean local field…

Cayley octad valuation-data reduction conjecture. The valuation data of $O$ determines the stable reduction type of $C/K$.

Cayley octad combinatorial reduction conjecture. Combinatorial data about the configuration of these eight points fully determines the stable reduction type of the curve, analogous…

Let $Q\subset\mathbb{P}^2$ be a real smooth plane quartic, let $L\subset\mathbb{P}^2$ be a line, and let $s_L(Q)$ denote the signed count … where $\operatorname{QType}_L(B)$ is the…

Let $V(Q)$ be a real quartic such that for each bitangent $L$, $L\cap V(Q)\cap L_\infty=\emptyset$, where $L_\infty$ denotes the line at infinity. For a real bitangent $L$, let…

Let $Q$ be a smooth plane quartic defined over $\mathbb{R}$, and let $L_\infty \subset \mathbb{P}^2_{\mathbb{R}}$ be a line defined over $\mathbb{R}$ such that…

Quadratic-points family conjecture. There is an infinite family $\mathcal{E}\subseteq\widetilde{\mathcal{M}_3^{\operatorname{Pl}}}(G)$ of $\mathbb{Q}$-isomorphism classes of smooth…

BLMPR conjecture. Each of the seven odd theta characteristics of $\Gamma$ is the specialization of four effective theta characteristics of $X$, counted with multiplicity.

Let $f$ be a smooth quartic on $\mathbb{P}^2_\mathbb{R}$, and let $S(f)$ be its Aronhold quartic. Aronhold quartic topology conjecture. If $f$ is hyperbolic, then $S(f)$ is either…