Introduction to Compact Riemann Surfaces and Dessins D'Enfants - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Compact Riemann Surfaces and Dessins D'Enfants write by Ernesto Girondo. This book was released on 2012. Introduction to Compact Riemann Surfaces and Dessins D'Enfants available in PDF, EPUB and Kindle. 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
Dessins d'Enfants on Riemann Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dessins d'Enfants on Riemann Surfaces write by Gareth A. Jones. This book was released on 2016-03-23. Dessins d'Enfants on Riemann Surfaces available in PDF, EPUB and Kindle. 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
Introduction to Compact Riemann Surfaces and Dessins d’Enfants - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Compact Riemann Surfaces and Dessins d’Enfants write by Ernesto Girondo. This book was released on 2011-12-22. Introduction to Compact Riemann Surfaces and Dessins d’Enfants available in PDF, EPUB and Kindle. 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.
The Grothendieck Theory of Dessins D'Enfants
The Grothendieck Theory of Dessins D'Enfants - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Grothendieck Theory of Dessins D'Enfants write by Leila Schneps. This book was released on 1994-07-28. The Grothendieck Theory of Dessins D'Enfants available in PDF, EPUB and Kindle. Dessins d'Enfants are combinatorial objects, namely drawings with vertices and edges on topological surfaces. Their interest lies in their relation with the set of algebraic curves defined over the closure of the rationals, and the corresponding action of the absolute Galois group on them. The study of this group via such realted combinatorial methods as its action on the Dessins and on certain fundamental groups of moduli spaces was initiated by Alexander Grothendieck in his unpublished Esquisse d'un Programme, and developed by many of the mathematicians who have contributed to this volume. The various articles here unite all of the basics of the subject as well as the most recent advances. Researchers in number theory, algebraic geometry or related areas of group theory will find much of interest in this book.
Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics
Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics write by Aaron Wootton. This book was released on 2022-02-03. Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics available in PDF, EPUB and Kindle. Automorphism groups of Riemann surfaces have been widely studied for almost 150 years. This area has persisted in part because it has close ties to many other topics of interest such as number theory, graph theory, mapping class groups, and geometric and computational group theory. In recent years there has been a major revival in this area due in part to great advances in computer algebra systems and progress in finite group theory. This volume provides a concise but thorough introduction for newcomers to the area while at the same time highlighting new developments for established researchers. The volume starts with two expository articles. The first of these articles gives a historical perspective of the field with an emphasis on highly symmetric surfaces, such as Hurwitz surfaces. The second expository article focuses on the future of the field, outlining some of the more popular topics in recent years and providing 78 open research problems across all topics. The remaining articles showcase new developments in the area and have specifically been chosen to cover a variety of topics to illustrate the range of diversity within the field.
