Donagi's Prym map injectivity conjecture

Let $\mathcal R_g$ be the moduli space of étale double covers $(\widetilde{C},C)$ of smooth curves, let $\operatorname{Cliff}(C)$ denote the Clifford index of $C$, and let $\mathscr P:\mathcal R_g\to\mathcal A_{g-1}$ be the Prym map. Define

$$U=\{(\widetilde{C},C)\in\mathcal R_g:\operatorname{Cliff}(C)\ge 3\}.$$

Donagi's conjecture. The restricted Prym map

$$\mathscr P|_U:U\to\mathcal A_{g-1}$$

is injective. This is a refinement of the generic Torelli problem for Prym varieties, restricting to covers whose base curve has Clifford index at least three. Generic injectivity is known for $g\ge 7$, but the precise locus on which the Prym map is injective remains the subject of the conjecture.