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Weierstrass semigroups on double covers of genus 4 curves. (English) Zbl 1395.14028
Summary: Let \(C\) be a complete non-singular irreducible curve of genus 4 over an algebraically closed field of characteristic 0. We determine all possible Weierstrass semigroups of ramification points on double covers of \(C\) which have genus greater than 11. Moreover, we construct double covers with ramification points whose Weierstrass semigroups are the possible ones.

MSC:
14H55 Riemann surfaces; Weierstrass points; gap sequences
14H30 Coverings of curves, fundamental group
14H45 Special algebraic curves and curves of low genus
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