Gauss-Prym maps on Enriques surfaces

Abstract

We prove that the k-th Gaussian map γ k H is surjective on a polarized unnodal Enriques surface (S, H) with ϕ(H) > 2k + 4. In particular, as a consequence, when ϕ(H) > 4(k + 2), we obtain the surjectivity of the k-th Gauss-Prym map γ k ω C ⊗α on smooth hyperplane sections C ∈ |H|. In case k = 1 it is sufficient to ask ϕ(H) > 6.