On the existence of Weierstrass points whose first non-gaps are five.
On Weierstrass points whose first non-gaps are four.
Cyclic coverings of an elliptic curve with two branch points and the gap sequences at the ramification points
Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve
2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14H40, 20M14. Let H be a 4-semigroup, i.e., a numerical semigroup whose minimum positive element is four. We denote by 4r(H) + 2 the minimum element of H which is congruent to 2 modulo 4. If the genus g of H is larger than 3r(H) − 1, then there is a cyclic covering π : C −→ P^1 of curves with degree 4 and its ramification point P such that the Weierstrass semigroup H(P) of P is H (Komeda [1]). In this paper it is...
Corrigendum for "Weierstrass Points with first Non-Gap four on a Double Covering of a Hyperelliptic Curve"
In the proof of Lemma 3.1 in [1] we need to show that we may take the two points p and q with p ≠ q such that p+q+(b-2)g21(C′)∼2(q1+… +qb-1) where q1,…,qb-1 are points of C′, but in the paper [1] we did not show that p ≠ q. Moreover, we hadn't been able to prove this using the method of our paper [1]. So we must add some more assumption to Lemma 3.1 and rewrite the statements of our paper after Lemma 3.1. The following is the correct version of Lemma 3.1 in [1] with its proof.
Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II
2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14J26. A 4-semigroup means a numerical semigroup whose minimum positive integer is 4. In [7] we showed that a 4-semigroup with some conditions is the Weierstrass semigroup of a ramification point on a double covering of a hyperelliptic curve. In this paper we prove that the above statement holds for every 4-semigroup.
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