Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve

Komeda, Jiryo, and Ohbuchi, Akira. "Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve." Serdica Mathematical Journal 30.1 (2004): 43-54. <http://eudml.org/doc/219643>.

@article{Komeda2004,
abstract = {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.},
author = {Komeda, Jiryo, Ohbuchi, Akira},
journal = {Serdica Mathematical Journal},
keywords = {Weierstrass Semigroup of a Point; Double Covering of a Hyperelliptic Curve; 4-Semigroup; Weierstrass semigroup of a point; 4-semigroup},
language = {eng},
number = {1},
pages = {43-54},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve},
url = {http://eudml.org/doc/219643},
volume = {30},
year = {2004},
}

TY - JOUR
AU - Komeda, Jiryo
AU - Ohbuchi, Akira
TI - Weierstrass Points with First Non-Gap Four on a Double Covering of a Hyperelliptic Curve
JO - Serdica Mathematical Journal
PY - 2004
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 30
IS - 1
SP - 43
EP - 54
AB - 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.
LA - eng
KW - Weierstrass Semigroup of a Point; Double Covering of a Hyperelliptic Curve; 4-Semigroup; Weierstrass semigroup of a point; 4-semigroup
UR - http://eudml.org/doc/219643
ER -