Daniel Ying - Academia.edu (original) (raw)

Papers by Daniel Ying

A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is... more A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann
sphere is called trigonal, and such a covering is called a trigonal morphism. Accola
showed that the trigonal morphism is unique for Riemann surfaces of genus g ≥ 5.
This thesis will characterize the Riemann surfaces of genus 4 with non-unique trigonal
morphism. We will describe the structure of the space of cyclic trigonal Riemann surfaces of genus 4.

Glasgow Mathematical Journal, 2009

A closed Riemann surface which can be realized as a three-sheeted covering of the Riemann sphere... more A closed Riemann surface which can be realized as a three-sheeted
covering of the Riemann sphere is called trigonal, and such a covering is called a
trigonal morphism. If the trigonal morphism is a cyclic regular covering, the Riemann
surface is called a cyclic trigonal Riemann surface. Using the characterization of cyclic
trigonality by Fuchsian groups, we find the structure of the space of cyclic trigonal
Riemann surfaces of genus 4.

Cambridge University Press eBooks, Jan 4, 2007

Groups St Andrews 2005 was held in the University of St Andrews in August 2005 and this first vol... more Groups St Andrews 2005 was held in the University of St Andrews in August 2005 and this first volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by Peter Cameron (Queen Mary, London) and Rostislav Grogorchuk (Texas A&amp;amp;M, USA). Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important.

Page 1. DI~EQTACIONE~ DEL ~EMINAQIO DE MATEMÁTICA~ fUNDAMENTALE~ 34 DANIELYING ON TRIGONAL RIEMAN... more Page 1. DI~EQTACIONE~ DEL ~EMINAQIO DE MATEMÁTICA~ fUNDAMENTALE~ 34 DANIELYING ON TRIGONAL RIEMANN SURFACES WIHT NON-UNIQUE MORPHISMS Page 2. On trigonal Riemann surfaces with non-unique morphims Daniel Ying May 25, 2005 Abstract. ...

Matematiska institutionen, 2006

I would also like to thank the foundation of Hierta-Retzius, the foundation of Knut and Alice Wal... more I would also like to thank the foundation of Hierta-Retzius, the foundation of Knut and Alice Wallenberg, and the foundation of G. S. Magnums. These foundations have contributed financially during my PhD. studies, enabling me to attend conferences and symposiums in my research area. At last, I would like to thank my family and friends for supporting me and always giving me the strength to carry on when I was in doubt. Thank you.

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

Riemann surfaces have an appealing feature to mathematicians (and hopefully to non-mathematicians... more Riemann surfaces have an appealing feature to mathematicians (and hopefully to non-mathematicians as well) in that they appear in a variety of mathematical fields. The point of the introduction of Riemann surfaces made by Riemann, Klein and Weyl (1851-1913), was that Riemann surfaces can be considered as both a one-dimensional complex manifold and an algebraic curve. Another possibility is to study Riemann surfaces as two-dimensional real manifolds, as Gauss (1822) had taken on the problem of taking a piece of a smooth oriented surface in Euclidean space and embedding it conformally into the complex plane. A fourth perspective came from the uniformisation theory of Klein, Poincaré and Koebe (1882-1907), who showed that every Riemann surface (which by ∗PhD Student at University of Linköping. E-mail: dayin@mai.liu.se, daniel@yings.se

Groups St Andrews 2005

Groups St Andrews 2005; was held in the University of St Andrews in August 2005 and this first vo... more Groups St Andrews 2005; was held in the University of St Andrews in August 2005 and this first volume of a two-volume book contains selected papers from the international conference. Four main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions by Peter Cameron (Queen Mary, London) and Rostislav Grogorchuk (Texas A&M, USA). Apart from the main speakers, refereed survey and research articles were contributed by other conference participants. Arranged in alphabetical order, these articles cover a wide spectrum of modern group theory. The regular Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past 25 years. Earlier volumes have had a major impact on the development of group theory and it is anticipated that this volume will be equally important.

In this thesis we will give a present survey of the various methods used in dealing with Riemann ... more In this thesis we will give a present survey of the various methods used in dealing with Riemann surfaces. Riemann surfaces are central in mathematics because of the multiple connections between complex analysis, algebraic geometry, hyperbolic geometry, group theory, topology etc. The main focus is the connection of holomorphic morphisms with branched coverings, and the use of permutation groups in classifying these morphisms.

manuscripta mathematica, 2005

A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is c... more A closed Riemann surface which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering will be called a trigonal morphism. If the trigonal morphism is a cyclic regular covering, the Riemann surface is called cyclic trigonal Riemann surface. Accola showed that the trigonal morphism is unique for Riemann surfaces of genus greater or equal to 5. Using the characterization of cyclic trigonality by Fuchsian groups given in [3], we obtain the Riemann surfaces of low genus with non-unique trigonal morphisms.

Glasgow Mathematical Journal, 2008

A closed Riemann surface which can be realized as a three-sheeted covering of the Riemann sphere ... more A closed Riemann surface which can be realized as a three-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. If the trigonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic trigonal Riemann surface. Using the characterization of cyclic trigonality by Fuchsian groups, we find the structure of the space of cyclic trigonal Riemann surfaces of genus 4.

Geometriae Dedicata, 2009

Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted cov... more Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. If the p-gonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic p-gonal Riemann surface. Accola showed that if the genus is greater than (p − 1) 2 the p-gonal morphism is unique. Using the characterization of p-gonality by means of Fuchsian groups we show that there exists a uniparametric family of cyclic p-gonal Riemann surfaces of genus (p−1) 2 which admit two p-gonal morphisms. In this work we show that these uniparametric families are connected spaces and that each of them is the Riemann sphere without three points. We study the Hurwitz space of pairs (X, f), where X is a Riemann surface in one of the above families and f is a p-gonal morphism, and we obtain that each of these Hurwitz spaces is a Riemann sphere without four points.

Disertaciones del Seminario de Matemáticas …, 2005

Revista de la Real …, 2007

A closed Riemann surface which is a 3-sheeted regular covering of the Riemann sphere is called cy... more 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.

Glasgow Mathematical Journal, 2009

Cambridge University Press eBooks, Jan 4, 2007

Matematiska institutionen, 2006

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

Groups St Andrews 2005

manuscripta mathematica, 2005

Glasgow Mathematical Journal, 2008

A closed Riemann surface which can be realized as a three-sheeted covering of the Riemann sphere ... more A closed Riemann surface which can be realized as a three-sheeted covering of the Riemann sphere is called trigonal, and such a covering is called a trigonal morphism. If the trigonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic trigonal Riemann surface. Using the characterization of cyclic trigonality by Fuchsian groups, we find the structure of the space of cyclic trigonal Riemann surfaces of genus 4.

Geometriae Dedicata, 2009

Disertaciones del Seminario de Matemáticas …, 2005

Revista de la Real …, 2007