Geodesic
Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve
Serdica Mathematical Journal, Tome 30 (2004) no. 1, pp. 43-54.

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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 showed that we can construct a double covering of a hyperelliptic curve and its ramification point P such that H(P) is equal to H even if g ≤ 3r(H) − 1.
Keywords: Weierstrass Semigroup of a Point, Double Covering of a Hyperelliptic Curve, 4-Semigroup 
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Komeda, Jiryo; Ohbuchi, Akira. Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve. Serdica Mathematical Journal, Tome 30 (2004) no. 1, pp. 43-54. http://geodesic.mathdoc.fr/item/SMJ2_2004_30_1_a3/