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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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