About this book
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.
Dessins d'enfants Riemann surfaces Algebraic curves Belyi functions Triangle groups Cartographic groups Quasiplatonic surfaces ABC problem
- DOI https://doi.org/10.1007/978-3-319-24711-3
- Copyright Information Springer International Publishing Switzerland 2016
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Print ISBN 978-3-319-24709-0
- Online ISBN 978-3-319-24711-3
- Series Print ISSN 1439-7382
- Series Online ISSN 2196-9922
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- Finance, Business & Banking