38 research outputs found
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