10 problems

Griffiths–Harris conjecture. For $3 \le r \le d$, every irreducible component of $\operatorname{NL}_{r,d}$ has codimension at least

Let $X_0: x_0^8+x_1^8+x_2^8+x_3^8=0$ be the Fermat octic, and let $C_1$ and $C_2$ be respectively a line, namely a complete intersection of type $(1,1)$, and a complete intersectio…

Let $\mathbf{NL}_g$ denote the space generated by Noether–Lefschetz cycles in the Chow ring of $\mathcal A_g$, and regard it as equipped with the relevant Hecke action. Pixton's mo…

Let $\overline{\mathcal M}_{g,1}(\pi,d)$ be the moduli space of log-stable maps of degree $d$ to the fibers of the universal family of elliptic curves, with evaluation map…

Let $\widetilde{\operatorname{NL}}_{g,d}$ be the stacks of homomorphisms from elliptic curves to principally polarized abelian varieties of degree $d$, and let their fundamental cl…

Let $\mathcal{A}_g$ be the moduli space of principally polarized abelian varieties of dimension $g$. Let…

Global equidistribution conjecture. The same estimate should hold when $S$ is quasi-projective of arbitrary dimension, which implies

Let $g=H_Y^2+1\geq 5$ be an odd integer, let $\mathcal F_g$ be the moduli space of polarized $K3$ surfaces of genus $g$, and let $\Sigma_g\subset\mathcal F_g$ be the naturally defi…

Let $X$ be a Calabi–Yau fourfold and let $\zeta\in \operatorname{Hg}^2(X)_{\mathrm{prim}}$ be a Hodge class. Let $Q_\zeta$ be the quadric on the relevant tangent space $T$ associat…

Let $S$ be a parameter space of a variation of Hodge structure, let $S_\zeta$ be the Noether–Lefschetz locus associated with a Hodge class $\zeta$, and suppose that the refined cod…