Weierstrass points and double converings of curves. With application: Symmetric numerical semigroup which cannot be realized as Weierstrass semigroups.
Weierstrass points and moduli of curves
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 showed that...
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.
When is a group homomorphism a covering homomorphism?