[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7468/jksmeb.2015.22.4.403

WEIERSTRASS SEMIGROUPS OF PAIRS ON H-HYPERELLIPTIC CURVES

KANG, EUNJU (DEPARTMENT OF INFORMATION AND COMMUNICATION TECHNOLOGY, HONAM UNIVERSITY)

Publication Information

The Pure and Applied Mathematics / v.22, no.4, 2015 , pp. 403-412 More about this Journal

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;

Citations & Related Records

Reference

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