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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.22 No.4

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Weierstrass semigroups of pairs on H-hyperelliptic curves

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.4, pp.403-412
https://doi.org/10.7468/jksmeb.2015.22.4.403
KANG, EUNJU
KANG,, E. (2015). Weierstrass semigroups of pairs on H-hyperelliptic curves. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(4), 403-412, https://doi.org/10.7468/jksmeb.2015.22.4.403

Abstract

Kato<xref>[6]</xref> and Torres<xref>[9]</xref> characterized the Weierstrass semigroup of ramification points on h-hyperelliptic curves. Also they showed the converse results that if the Weierstrass semigroup of a point P on a curve C satisfies certain numerical condition then C can be a double cover of some curve and P is a ramification point of that double covering map. In this paper we expand their results on the Weierstrass semigroup of a ramification point of a double covering map to the Weierstrass semigroup of a pair (P, Q). We characterized the Weierstrass semigroup of a pair (P, Q) which lie on the same fiber of a double covering map to a curve with relatively small genus. Also we proved the converse: if the Weierstrass semigroup of a pair (P, Q) satisfies certain numerical condition then C can be a double cover of some curve and P, Q map to the same point under that double covering map.

keywords
Weierstrass semigroup of a pair, Weierstrass semigroup of a point, double covering map

Reference

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Torres, F.;. (1994). Weierstrass points and double coverings of curves with application: Symmetric numerical semigroups which cannot be realized as Weierstrass semigroups. Manuscripta Math., 83, 39-58. 10.1007/BF02567599.

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Kato, T.;. (1979). On criteria of &#x11F;-hyperellipticity. Kodai Math. J., 2, 275-285. 10.2996/kmj/1138036022.

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Kang, E.;Kim, S.J.;. (2003). Special pairs in the generating subset of the Weierstrass semigroup at a pair. Geom. Dedicata, 99(1), 167-177. 10.1023/A:1024960704513.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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