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arXiv · 2206.02430

Gauss-Prym maps on Enriques surfaces

Dario Faro·Irene Spelta
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Abstract

We prove that the $k$-th Gaussian map $\gamma^k_{H}$ is surjective on a polarized unnodal Enriques surface $(S, H)$ with $\phi(H)>2k+4$. In particular, as a consequence, when $\phi(H)>4(k+2)$, we obtain the surjectivity of the $k$-th Gauss-Prym map $\gamma^k_{\omega_C\otimes\alpha}$ on smooth hyperplane sections $C\in \vert H\vert.$ In case $k=1$ it is sufficient to ask $\phi(H)>6$.

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Dario Faro, Irene Spelta. 2022-06-06. Gauss-Prym maps on Enriques surfaces. https://doi.org/10.1002/mana.202200287

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