Introduction to compact Riemann surfaces and dessins d"enfants
 298 Pages
 2012
 4.96 MB
 617 Downloads
 English
Cambridge University Press , Cambridge, New York
Riemann surfaces, Dessins d"enfants (Mathema
Statement  Ernesto Girondo, Gabino GonzálezDiez 
Series  London Mathematical Society student texts  79 
Contributions  GonzálezDiez, Gabino 
Classifications  

LC Classifications  QA333 .G57 2012 
The Physical Object  
Pagination  xii, 298 p. : 
ID Numbers  
Open Library  OL25570677M 
ISBN 10  0521519632, 0521740223 
ISBN 13  9780521519632, 9780521740227 
OCLC/WorldCa  778324075 



Second annual report of the chief commissioner of public works, 1856
342 Pages4.78 MB1709 DownloadsFormat: FB2 

An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi–Grothendieck theory of dessins d'enfants.
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Book Description Starting with a friendly account of the theory of compact Riemann surfaces, this book then introduces the BelyiGrothendieck theory of dessins d'enfants, taking the reader with no Cited by: Introduction to compact Riemann surfaces and dessins d'enfants.
Summary: Starting with a friendly account of the theory of compact Riemann surfaces, this book then introduces the BelyiGrothendieck theory of dessins d'enfants, taking the reader with no previous knowledge of the subject to the forefront of current research. Few books on the subject of Riemann surfaces Introduction to compact Riemann surfaces and dessins denfants book the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the.
Introduction to Compact Riemann Surfaces and Dessins d’Enfants Ernesto Girondo, Gabino GonzálezDiez 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 s and is now an active field of research.
Description Introduction to compact Riemann surfaces and dessins d"enfants EPUB
Topology of Riemann surfaces 26 Curves, function fields and Riemann surfaces 67 2 Riemann surfaces and discrete groups 81 Uniformization 81 The existence of meromorphic functions Fuchsian groups Fuchsian triangle groups Automorphisms of Riemann surfaces The moduli space of compact Riemann surfaces Introduction to Compact Riemann Surfaces and Dessins d Enfants In this 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.
Dessins d'Enfants on Riemann Surfaces Gareth A. Jones, Jürgen Wolfart (auth.) 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. This chapter begins with a brief historical introduction to the theory of dessins d’enfants, from the early discovery of the platonic solids, through nineteenthcentury work on Riemann surfaces.
Introduction This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L ² method, a powerful technique used in the theory of several complex variables. This chapter begins with a brief historical introduction to the theory of dessins d’enfants, from the early discovery of the platonic solids, through nineteenthcentury work on Riemann surfaces, algebraic curves and holomorphic functions, and twentiethcentury research on regular maps, to the fundamental and farreaching ideas circulated by Grothendieck in the s, and subsequent.
For compact Riemann surfaces, there are clear treatments of divisors, Weierstrass points, the RiemannRoch theorem and other important topics.
Details Introduction to compact Riemann surfaces and dessins d"enfants EPUB
Springer's book is an excellent text for an introductory course on Riemann surfaces. It includes exercises after each chapter and is illustrated with a beautiful set of s: 3.
Riemann surfaces and algebraic curves 2. Riemann surfaces and Fuchsian groups 3. Belyi's theorem 4. Dessins d'enfants References Index. "Compact Riemann Surfaces: An Introduction to Contemporary Mathematics starts off with a wonderful Preface containing a good deal of history, as well as Jost’s explicit dictum that there are three foci around which the whole subject revolves.
Jost’s presentation is quite accessible, modulo a lot of diligence on the part of the reader. 78 Clifford algebras: An introduction, D. GARLING 79 Introduction to compact Riemann surfaces and dessins d enfants, ERNESTO GIRONDO & GABINO GONZÁLEZDIEZ 80 The Riemann hypothesis for function elds, MACHIEL VAN FRANKENHUIJSEN 81 Number theory, Fourier analysis and geometric discrepancy, GIANCARLO TRAVAGLINI.
Product Information. 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. Dessin d’enfants is the french word for children’s drawing and means a type of bipartite graph embedded in a compact oriented surface. One of the results you can learn about in this seminar says that a dessin imposes a canonical complex structure on the surrounding surface, and that the resulting compact Riemann surface is actually an.
They deal with the study of bipartite graphs on Riemann surfaces known as dessins d'enfants, a term coined by A. Grotendieck. These are simple characterizations of certain maps on Riemann surfaces. Knowledge of complex functions, Riemann surfaces and group theory are prerequisites.
The book has 3. Web page of the reseach group of the Universidad Autónoma of Madrid on compact Riemann surfaces.
Books: Introduction to compact Riemann surfaces and dessins d'enfants E. Girondo, G. GonzálezDiez London Mathematical Society Student Texts, 79 Cambridge University Press, Cambridge, xii+ pp.
ISBN: ; Geometry of Riemann. Dessin d’enfants are a type of graph embedded in an oriented surface which are used to study Riemann surfaces and provide invariants for the action of the absolute Galois group. Dessin d’enfants date back towhen they were used by William Hamilton in his work Icosian Calculus.
The German mathematician Felix Klein used a relatively. We will mainly continue our learning seminar on Dessins d' follow the following book: Girondo and GonzalezDiez, Introduction to Compact Riemann Surfaces and Dessins d'Enfants, London Mathematical Society Student Te Cambridge University Press, Although Riemann surfaces are a timehonoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics.
It 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.
Book Description: 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. ”A compact Riemann surface Sis defined over a number field if and only if there exists Key Words: Riemann Surfaces, Dessin d’enfants, cohomology, Riemann.
Universidade de Lisboa Resumo Faculdade de Ciências Matemática Introduction Riemann Surfaces. 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. In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers.
1 Compact Riemann surfaces and algebraic curves Basic deﬁnitions Riemann surfaces – examples Deﬁnition A topological surface X is a Hausdorﬀ topologi cal space provided with a collection {ϕ i: U i −→ϕ i(U i)}of home omorphisms (called charts) from open subsets U i ⊂X (called coordinate neighbourhoods) to open subsets ϕ i(U i) ⊂C such that.
Girondo, G. GonzálezDiez, Introduction to compact Riemann surfaces and dessins d’enfants, London Mat. Soc. Student Te Cambridge Univ.
Press xii+ pp. References on the history of dessins d’enfants. Lieven Le Bruyn, Klein’s dessins d’enfant and the buckyball, web. From the reviews: “The present book gives a solid introduction to the theory of both compact and noncompact Riemann surfaces.
While modern introductions often take the view point of algebraic geometry, the present book tries to also cover the analytical aspects. We will cover the text "Introduction to Compact Riemann Surfaces and Dessins d’Enfants" (London Mathematical Society Student Texts) by Ernesto Girondo and Gabino GonzalezDiez.
Structure of the seminar: Our main reference is the book \Introduction to Compact Riemann Surfaces and Dessins d’Enfants" of Girondo and Gonz alezDiez [GGD]. It is available as an eBook if you search for it via the website of the library in Dusseldorf. It is easy to read and contains a lot of examples.
Our main interest lies in Chapter 4. are Girondo and GonzalezDiez’s Introduction to Compact Riemann Surfaces and Dessins d’Enfants [3] (for the ﬁrst two parts) and Lando and Zvonkin’s Graphs on Surfaces and Their Applications [8] (for the third).
Future versions of this paper are anticipated to include a fourth part on the action of Gal(Q=Q) on dessins d’enfants.2.
Dessins d’enfants In this section we review the basics of dessins d’enfants based on [10]. A dessin, or dessin d’enfant, is de ned to be a bipartite graph (with nitely many black and white vertices) embedded on a Riemann surface, which we will assume throughout to be compact and connected.
Suppose a vertex von a dessin has 1.dessins d’enfants and, by Belyi’s theorem, there is a natural action of the absolute Galois Mathematics Subject Classiﬁcation.
30F10, 14H37, 14H Key wor ds and phrases.