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WEIERSTRASS SEMIGROUPS OF PAIRS ON H-HYPERELLIPTIC CURVES
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  • Journal title : The Pure and Applied Mathematics
  • Volume 22, Issue 4,  2015, pp.403-412
  • Publisher : Korea Society of Mathematical Education
  • DOI : 10.7468/jksmeb.2015.22.4.403
 Title & Authors
WEIERSTRASS SEMIGROUPS OF PAIRS ON H-HYPERELLIPTIC CURVES
KANG, EUNJU;
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 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;
 Language
English
 Cited by
 References
1.
R.D.M. Accola: Topics in the Theory of Riemann Surfaces. Lecture Notes in Math 1595. Springer-Verlag, Berlin (1994).

2.
E. Arbarello, M. Cornalba, P.A. Griffiths & J. Harris: Geometry of Algebraic Curves, I. Springer-Verlag, Berlin/New York (1985).

3.
H.M. Farkas & I. Kra: Riemann Surfaces. Graduate Texts in Mathematics 71, Springer-Verlag, New York (1980).

4.
M. Homma: The Weierstrass semigroup of a pair of points on a curve. Arch. Math. 67 (1996), 337-348. crossref(new window)

5.
E. Kang & S.J. Kim: Special pairs in the generating subset of the Weierstrass semigroup at a pair. Geom. Dedicata 99 (2003), no. 1, 167-177. crossref(new window)

6.
T. Kato: On criteria of -hyperellipticity. Kodai Math. J. 2 (1979), 275-285. crossref(new window)

7.
S.J. Kim: On the index of the Weierstrass semigroup of a pair of points on a curve. Arch. Math. 62 (1994), 73-82. crossref(new window)

8.
S.J. Kim & J. Komeda: Weierstrass semigroups of pairs of points whose first non-gaps are three. Geom. Dedicata 93 (2002), no. 1, 113-119. crossref(new window)

9.
F. Torres: Weierstrass points and double coverings of curves with application: Symmetric numerical semigroups which cannot be realized as Weierstrass semigroups. Manuscripta Math. 83 (1994), 39-58. crossref(new window)