We prove that the moduli space of double covers ramified at two points Rg,2 is uniruled for 3 ≤ g ≤ 6 and of general type for g ≥ 16. Furthermore, we consider Prymcanonical divisorial strata in the moduli space CnRg parametrizing n-pointed Prym curves, and we compute their classes in PicQ(CnRg).
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