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Title: Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve
Authors: Komeda, Jiryo
Ohbuchi, Akira
Keywords: Weierstrass Semigroup of a Point
Double Covering of a Hyperelliptic Curve
Issue Date: 2004
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 30, No 1, (2004), 43p-54p
Abstract: 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.
Description: 2000 Mathematics Subject Classification: Primary 14H55; Secondary 14H30, 14H40, 20M14.
ISSN: 1310-6600
Appears in Collections:Volume 30 Number 1

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