Weierstrass semigroups of pairs on H-hyperelliptic curves
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Kato[6] and Torres[9] characterized the Weierstrass semigroup of rami-fication 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 Weier- strass 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.
Abstract
Kato[6] and Torres[9] characterized the Weierstrass semigroup of rami- fication 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 Weier- strass 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.
참고문헌 (9)
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