Geodesic
Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve II
Serdica Mathematical Journal, Tome 34 (2008) no. 4, pp. 771-782.

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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.
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 II. Serdica Mathematical Journal, Tome 34 (2008) no. 4, pp. 771-782. http://geodesic.mathdoc.fr/item/SMJ2_2008_34_4_a4/