바로가기메뉴

본문 바로가기 주메뉴 바로가기
 

logo

  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

Article Contents

Prev
e-Submission

Vol.22 No.4

PDF Citation Share

Weierstrass semigroups of pairs on H-hyperelliptic curves

Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
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, 22(4), 403-412, https://doi.org/10.7468/jksmeb.2015.22.4.403

Abstract

Kato[6] and Torres[9] 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

1.

Arbarello, E.;Cornalba, M.;Griffiths, P.A.;Harris, J.;. Geometry of Algebraic Curves.

2.

Accola, R.D.M.;. Topics in the Theory of Riemann Surfaces.

3.

Homma, M.;. (1996). The Weierstrass semigroup of a pair of points on a curve. Arch. Math., 67, 337-348. 10.1007/BF01197599.

4.

Farkas, H.M.;Kra, I.;. Riemann Surfaces;Graduate Texts in Mathematics.

5.

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.

6.

Kim, S.J.;Komeda, J.;. (2002). Weierstrass semigroups of pairs of points whose first non-gaps are three. Geom. Dedicata, 93(1), 113-119. 10.1023/A:1020301422774.

7.

Kim, S.J.;. (1994). On the index of the Weierstrass semigroup of a pair of points on a curve. Arch. Math., 62, 73-82. 10.1007/BF01200442.

8.

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

9.

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: Theoretical Mathematics and Pedagogical Mathematics

e-Submission OA Policy