8 problems

Let $S$ be a surface given in ${\bf{TK1}}$, ${\bf{TK2}}$, or ${\bf{TK3}}$. Let $F$ and $C$ denote the divisor classes used in these trigonal K3 surface constructions, and let $l$ b…

Geometric height pairing and Lear extension conjecture. There is a canonical isomorphism of $\mathbb{Q}$-line bundles over $\overline{S}$:

Hodge endomorphism field conjecture. (1) If $E$ is neither $\mathbb{Q}$ nor an imaginary quadratic field, then $X_0$ is of Type I. (2) If $E\neq\mathbb{Q}$, then $X_0$ is either of…

Kulikov model existence conjecture. Any K3 surface over $K$ admits a Kulikov model after replacing $K$ by a finite extension.

Let $G$ be a complex reductive group and let $X$ be a smooth complex projective curve. Let $\mathcal Shv_{\mathcal N}(Bun_G(X))$ be the Betti category of nilpotent sheaves. Automor…

Let $g$ be the genus of a hyperelliptic curve, let $\bm{\sigma}(u)$ be its genus-$g$ hyperelliptic sigma-function, and let $\Lambda_{g-1}$ be a parameter stratum on which the genus…

Let $X$ be a smooth toric variety, and let $\Delta_t$ be a family of toric $\mathbb{Q}$-divisors with coefficients less than $1$, affine in $t\in(0,1]$, converging to a reduced div…

Dimension-function conjecture. The equivalence relation induced on ${\mathcal Y}_{\operatorname{init} f}$ by $\pi_{f,\operatorname{init}}$ can be determined from this function as t…