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Curves on weighted \(K3\) surfaces of degree two with symmetric Weierstrass semigroups. (English) Zbl 07196525
Summary: Let \(C\) be a curve on the weighted projective plane \(\mathbb{P}(1, 1, 4)\) which is of Fermat type or almost Fermat type. We construct \(K3\) surfaces which are double covers of \(\mathbb{P}(1, 1, 4)\) and which contain pointed curves with symmetric Weierstrass semigroups which are double covers of \(C\).
MSC:
14H55 Riemann surfaces; Weierstrass points; gap sequences
14H50 Plane and space curves
14H30 Coverings of curves, fundamental group
20M14 Commutative semigroups
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