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

Serdica Mathematical Journal (2004)

- Volume: 30, Issue: 1, page 43-54
- ISSN: 1310-6600

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topKomeda, 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 -

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