Cover of: Introduction to compact Riemann surfaces and dessins d

Introduction to compact Riemann surfaces and dessins d"enfants

  • 298 Pages
  • 4.96 MB
  • 617 Downloads
  • English
by
Cambridge University Press , Cambridge, New York
Riemann surfaces, Dessins d"enfants (Mathema
StatementErnesto Girondo, Gabino González-Diez
SeriesLondon Mathematical Society student texts -- 79
ContributionsGonzález-Diez, Gabino
Classifications
LC ClassificationsQA333 .G57 2012
The Physical Object
Paginationxii, 298 p. :
ID Numbers
Open LibraryOL25570677M
ISBN 100521519632, 0521740223
ISBN 139780521519632, 9780521740227
OCLC/WorldCa778324075

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 Belyi-Grothendieck 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 Belyi-Grothendieck 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 González-Diez 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 nineteenth-century 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 nineteenth-century work on Riemann surfaces, algebraic curves and holomorphic functions, and twentieth-century research on regular maps, to the fundamental and far-reaching ideas circulated by Grothendieck in the s, and subsequent.

For compact Riemann surfaces, there are clear treatments of divisors, Weierstrass points, the Riemann-Roch 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 GONZÁLEZ-DIEZ 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. González-Diez 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 Gonzalez-Diez, Introduction to Compact Riemann Surfaces and Dessins d'Enfants, London Mathematical Society Student Te Cambridge University Press, Although Riemann surfaces are a time-honoured 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. González-Diez, 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 non-compact 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 Gonzalez-Diez.

Structure of the seminar: Our main reference is the book \Introduction to Compact Rie-mann Surfaces and Dessins d’Enfants" of Girondo and Gonz alez-Diez [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 Gonzalez-Diez’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.