Weierstrass Semigroup of a Point Double Covering of a Hyperelliptic Curve 4-Semigroup
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.
