Abstract
We give a geometric construction of sub-linear systems on a K3 surface consisting of smooth curves C with infinitely many \({g^1_{{\rm gon}(C)}}\)’s.
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Acknowledgements
The proof of this theorem is due to some interesting conversations with Gian Pietro Pirola for the case H 2 = 4, i.e., when S is a quartic surface in \({\mathbb{P}^{3}}\). Thanks also to Andreas Leopold Knutsen for valuable comments.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Rasmussen, N.H.W. New examples of curves with a one-dimensional family of pencils of minimal degree. Arch. Math. 97, 135–140 (2011). https://doi.org/10.1007/s00013-011-0288-4
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DOI: https://doi.org/10.1007/s00013-011-0288-4