Kim, Seon Jeong; Komeda, Jiryo Weierstrass semigroups on double covers of genus 4 curves. (English) Zbl 1395.14028 J. Algebra 405, 142-167 (2014). 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. Cited in 3 Documents MSC: 14H55 Riemann surfaces; Weierstrass points; gap sequences 14H30 Coverings of curves, fundamental group 14H45 Special algebraic curves and curves of low genus Keywords:Weierstrass semigroup of a point; double cover of a curve; curve of genus 4 PDF BibTeX XML Cite \textit{S. J. Kim} and \textit{J. Komeda}, J. Algebra 405, 142--167 (2014; Zbl 1395.14028) Full Text: DOI References: [1] Coppens, M., The Weierstrass gap sequence of the ordinary ramification points of trigonal coverings of \(\mathbb{P}^1\); existence of a kind of Weierstrass gap sequence, J. Pure Appl. Algebra, 43, 11-25, (1986) · Zbl 0616.14012 [2] Komeda, J., On Weierstrass points whose first non-gaps are four, J. Reine Angew. Math., 341, 68-86, (1983) · Zbl 0498.30053 [3] Komeda, J., A numerical semigroup from which the semigroup gained by dividing by two is either \(\mathbb{N}_0\) or a 2-semigroup or \(\langle 3, 4, 5 \rangle\), Res. Rep. Kanagawa Inst. Technol. Part B, 33, 37-42, (2009) [4] Komeda, J., Double coverings of curves and non-Weierstrass semigroups, Comm. Algebra, 41, 312-324, (2013) · Zbl 1270.14014 [5] Komeda, J., On Weierstrass semigroups of double coverings of genus three curves, Semigroup Forum, 83, 479-488, (2011) · Zbl 1244.14025 [6] Komeda, J.; Ohbuchi, A., On double coverings of a pointed non-singular curve with any Weierstrass semigroup, Tsukuba J. Math., 31, 205-215, (2007) · Zbl 1154.14023 [7] Komeda, J.; Ohbuchi, A., Weierstrass points with first non-gap four on a double covering of a hyperelliptic curve II, Serdica Math. J., 34, 771-782, (2008) · Zbl 1224.14008 [8] Oliveira, G.; Pimentel, F. L.R., On Weierstrass semigroups of double covering of genus two curves, Semigroup Forum, 77, 152-162, (2008) · Zbl 1161.14023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.