Introduction to Compact Riemann Surfaces and Dessins D'Enfants
Title | Introduction to Compact Riemann Surfaces and Dessins D'Enfants PDF eBook |
Author | Ernesto Girondo |
Publisher | Cambridge University Press |
Pages | 311 |
Release | 2012 |
Genre | Mathematics |
ISBN | 0521519632 |
An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi-Grothendieck theory of dessins d'enfants.
Dessins d'Enfants on Riemann Surfaces
Title | Dessins d'Enfants on Riemann Surfaces PDF eBook |
Author | Gareth A. Jones |
Publisher | Springer |
Pages | 264 |
Release | 2016-03-23 |
Genre | Mathematics |
ISBN | 3319247115 |
This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces. The first part of the book presents basic material, guiding the reader through the current field of research. A key point of the second part is the interplay between the automorphism groups of dessins and their Riemann surfaces, and the action of the absolute Galois group on dessins and their algebraic curves. It concludes by showing the links between the theory of dessins and other areas of arithmetic and geometry, such as the abc conjecture, complex multiplication and Beauville surfaces. Dessins d'Enfants on Riemann Surfaces will appeal to graduate students and all mathematicians interested in maps, hypermaps, Riemann surfaces, geometric group actions, and arithmetic.
Introduction to Compact Riemann Surfaces and Dessins d’Enfants
Title | Introduction to Compact Riemann Surfaces and Dessins d’Enfants PDF eBook |
Author | Ernesto Girondo |
Publisher | Cambridge University Press |
Pages | 311 |
Release | 2011-12-22 |
Genre | Mathematics |
ISBN | 1139504185 |
Few books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this 2011 book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then use this knowledge to introduce the reader to the theory of dessins d'enfants and its connection with algebraic curves defined over number fields. A large number of worked examples are provided to aid understanding, so no experience beyond the undergraduate level is required. Readers without any previous knowledge of the field of dessins d'enfants are taken rapidly to the forefront of current research.
Compact Riemann Surfaces
Title | Compact Riemann Surfaces PDF eBook |
Author | Jürgen Jost |
Publisher | Springer Science & Business Media |
Pages | 304 |
Release | 2013-04-17 |
Genre | Mathematics |
ISBN | 3662034468 |
This book is novel in its broad perspective on Riemann surfaces: the text systematically explores the connection with other fields of mathematics. The book can serve as an introduction to contemporary mathematics as a whole, as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. The book is unique among textbooks on Riemann surfaces in its inclusion of an introduction to Teichmüller theory. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants
Title | Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants PDF eBook |
Author | Frank Neumann |
Publisher | Springer Nature |
Pages | 240 |
Release | 2020-09-26 |
Genre | Mathematics |
ISBN | 3030517950 |
This book presents original peer-reviewed contributions from the London Mathematical Society (LMS) Midlands Regional Meeting and Workshop on 'Galois Covers, Grothendieck-Teichmüller Theory and Dessinsd'Enfants', which took place at the University of Leicester, UK, from 4 to 7 June, 2018. Within the theme of the workshop, the collected articles cover a broad range of topics and explore exciting new links between algebraic geometry, representation theory, group theory, number theory and algebraic topology. The book combines research and overview articles by prominent international researchers and provides a valuable resource for researchers and students alike.
An Introduction to Riemann Surfaces
Title | An Introduction to Riemann Surfaces PDF eBook |
Author | Terrence Napier |
Publisher | Springer Science & Business Media |
Pages | 563 |
Release | 2011-09-08 |
Genre | Mathematics |
ISBN | 0817646930 |
This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method. This method is a powerful technique from the theory of several complex variables, and provides for a unique approach to the fundamentally different characteristics of compact and noncompact Riemann surfaces. The inclusion of continuing exercises running throughout the book, which lead to generalizations of the main theorems, as well as the exercises included in each chapter make this text ideal for a one- or two-semester graduate course.
Compact Riemann Surfaces And Algebraic Curves
Title | Compact Riemann Surfaces And Algebraic Curves PDF eBook |
Author | Kichoon Yang |
Publisher | World Scientific |
Pages | 184 |
Release | 1988-11-01 |
Genre | Mathematics |
ISBN | 9814520039 |
This volume is an introduction to the theory of Compact Riemann Surfaces and algebraic curves. It gives a concise account of the elementary aspects of different viewpoints in curve theory. Foundational results on divisors and compact Riemann surfaces are also stated and proved.