13 problems

Let $p$ be an odd prime, and let $X$ be a smooth curve of genus $3$ over $\overline{\mathbf F}_p$. An unramified double cover of $X$ is a degree-two étale morphism $\pi:Y\to X$; by…

The Prym characterization by the minimal number of conditions. Then $n\geq 2g$, and equality characterizes Prym varieties. This is proposed as a higher Castelnuovo–Schottky problem…

Let $(P,\Xi)$ be a Prym variety associated with a double cover $\pi:\widetilde C\to C$, and let $\Sigma$ be the relevant Prym-theta subvariety. Let $\Gamma_{00}'$ consist of sectio…

Let $X$ be a principally polarized Abelian variety with theta function $\theta$. Let $\widehat{\theta}_1$ denote the Prym theta function associated with the first involution, let…

Let $R_{\widetilde{G}/G}$ be the cone associated with a double cover $\widetilde{G}\to G$. As a double cover of tropical curves $\widetilde{\Gamma}\to\Gamma$ varies over…

The tropical Poincaré–Prym formula. The cycle class of $\widetilde{Y}_d$ satisfies

Let $\mathcal{R}_6$ be the moduli space of Prym curves of genus $6$, let $\mathcal{A}_5$ be the moduli space of principally polarized abelian varieties of dimension $5$, and let…

Let $C$ be a curve of genus $2$ or $3$ over a number field $K$, with an unramified double cover … and associated Prym variety $\operatorname{Prym}(D/C)$ over $K$. Let…

Let $S'$ be a K3 surface that is a branched double cover of a degree-one del Pezzo surface $T'$, and let $D'$ be a genus-two curve on $T'$ covered by a genus-five curve $C'$ on…

Prym-Green conjecture. The resolution of a general level $\ell$ paracanonical curve of genus $g$ is natural.

Prym tropicalization conjecture. The skeleton of the Prym variety associated with $f$ is the tropical Prym variety associated with $\phi$; equivalently, the Prym construction commu…

Donagi's conjecture. The restricted Prym map

Let $p:C\overset{\pi}{\longrightarrow}C'\overset{g}{\longrightarrow}\mathbb{P}^1$ be a simply ramified covering of type $B_n$. Let $P(C,C')$ be its Prym variety, let $P(X,\delta)$…