On the Difference of 4-Gonal Linear Systems on some Curves

Let C = (C, g^1/4 ) be a tetragonal curve. We consider the scrollar invariants e1 , e2 , e3 of g^1/4 . We prove that if W^1/4 (C) is a non-singular variety, then every g^1/4 ∈ W^1/4 (C) has the same scrollar invariants

The Weierstrass semigroups on double covers of genus two curves

We show that three numerical semigroups , and are of double covering type, i.e., the Weierstrass semigroups of ramification points on double covers of curves. Combining this with the results of Oliveira-Pimentel and Komeda we can determine the Weierstrass semigroups of the ramification points on double covers of genus two curves.Comment: 5 page

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

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 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.* Partially supported by Grant-in-Aid for Scientific Research (15540051), Japan Society for the Promotion of Science. ** Partially supported by Grant-in-Aid for Scientific Research (15540035), Japan Society for the Promotion of Science

On γ-Hyperelliptic Weierstrass Semigroups of Genus 6γ + 1 and 6γ

Let (C, P) be a pointed non-singular curve such that the Weierstrass semigroup H(P) of P is a γ-hyperelliptic numerical semigroup. Torres showed that there exists a double covering π : C → C‘ such that the point P is a ramification point of π if the genus g of C is larger than or equal to 6γ + 4. Kato and the authors also showed that the same result holds in the case g = 6γ + 3 or 6γ + 2. In this paper we prove that there exists a double covering π : C → C’ satisfying the above condition even if g = 6γ + 1, 6γ and H(P) does not contain 4

On Some Numerical Relations of tetragonal Linear Systems

Let L be a pencil of degree 4 on a curve C and let e_1, e_2, e_3 be scrolar invariants. We prove that [numerical formula] if and only if e_1, e_2, e_3 are scrollar invariants of some tetragonal curve

On the Normal Generation of Ample Line Bundles on Abelian Varieties Defined Over Some Special Field

Let L be an ample line bundle on an abelian variety A defined over an algebraically closed field k. We already know that L is normally generated if L is base point free and char (k)≠2. In this article, we prove that the above result is also true if char (k)=2

On Some Numerical Relations of d-gonal Linear Systems

Let L be a pencil of degree d on a curve C and let e_1・・・, e_ be scrolar invariants. We already prove that [numerical formula], ...d-2 if [numerical formula] is birationally very ample. In this article, we extend the above result

On the Construction of a Special Divisor of Some Special Curve

Let π: X→C be a triple covering of curves where C is Brill-Noether general. We prove the existence of a base point free pencil of degree [numerical formula] on a curve X which is not composed with π