Gauss‐Prym maps on Enriques surfaces

Dario Faro and Irene Spelta

Mathematische Nachrichten, 2023, vol. 296, issue 9, 4454-4462

Abstract: We prove that the kth Gaussian map γHk$\gamma ^k_{H}$ is surjective on a polarized unnodal Enriques surface (S,H)$(S, H)$ with φ(H)>2k+4$\varphi (H)>2k+4$. In particular, as a consequence, when φ(H)>4(k+2)$\varphi (H)>4(k+2)$, we obtain the surjectivity of the kth Gauss‐Prym map γωC⊗αk$\gamma ^k_{\omega _C\otimes \alpha }$, with α:=ωS|C$\alpha :=\omega _{S\vert _{C}}$, on smooth hyperplane sections C∈|H|$C\in \vert H\vert$. In case k=1$k=1$, it is sufficient to ask φ(H)>6$\varphi (H)>6$.

Date: 2023
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