# On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.

Antonio F. Costa; Milagros Izquierdo; Daniel Ying

RACSAM (2007)

- Volume: 101, Issue: 1, page 81-86
- ISSN: 1578-7303

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topCosta, Antonio F., Izquierdo, Milagros, and Ying, Daniel. "On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.." RACSAM 101.1 (2007): 81-86. <http://eudml.org/doc/41666>.

@article{Costa2007,

abstract = {A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cyclic trigonal, and such a covering is called a cyclic trigonal morphism. Accola showed that if the genus is greater or equal than 5 the trigonal morphism is unique. Costa-Izquierdo-Ying found a family of cyclic trigonal Riemann surfaces of genus 4 with two trigonal morphisms. In this work we show that this family is the Riemann sphere without three points. We also prove that the Hurwitz space of pairs (X, f), with X a surface of the above family and f a trigonal morphism, is the Riemann sphere with four punctures. Finally, we give the equations of the curves in the family.},

author = {Costa, Antonio F., Izquierdo, Milagros, Ying, Daniel},

journal = {RACSAM},

language = {eng},

number = {1},

pages = {81-86},

title = {On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.},

url = {http://eudml.org/doc/41666},

volume = {101},

year = {2007},

}

TY - JOUR

AU - Costa, Antonio F.

AU - Izquierdo, Milagros

AU - Ying, Daniel

TI - On the family of cyclic trigonal Riemann surfaces of genus 4 with several trigonal morphisms.

JO - RACSAM

PY - 2007

VL - 101

IS - 1

SP - 81

EP - 86

AB - A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cyclic trigonal, and such a covering is called a cyclic trigonal morphism. Accola showed that if the genus is greater or equal than 5 the trigonal morphism is unique. Costa-Izquierdo-Ying found a family of cyclic trigonal Riemann surfaces of genus 4 with two trigonal morphisms. In this work we show that this family is the Riemann sphere without three points. We also prove that the Hurwitz space of pairs (X, f), with X a surface of the above family and f a trigonal morphism, is the Riemann sphere with four punctures. Finally, we give the equations of the curves in the family.

LA - eng

UR - http://eudml.org/doc/41666

ER -

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