Geometry Of Riemann Surfaces

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Geometry Of Riemann Surfaces

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Author : William J. Harvey
language : en
Publisher: Cambridge University Press
Release Date : 2010-02-11

Geometry Of Riemann Surfaces written by William J. Harvey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-02-11 with Mathematics categories.

Original research and expert surveys on Riemann surfaces.

Geometry And Spectra Of Compact Riemann Surfaces

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Author : Peter Buser
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-29

Geometry And Spectra Of Compact Riemann Surfaces written by Peter Buser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-29 with Mathematics categories.

This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.

Compact Riemann Surfaces

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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-13

Compact Riemann Surfaces written by Jürgen Jost and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-13 with Mathematics categories.

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.

Algebraic Curves And Riemann Surfaces

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Author : Rick Miranda
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Algebraic Curves And Riemann Surfaces written by Rick Miranda and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.

Riemann Surfaces By Way Of Complex Analytic Geometry

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Author : Dror Varolin
language : en
Publisher: American Mathematical Soc.
Release Date :

Riemann Surfaces By Way Of Complex Analytic Geometry written by Dror Varolin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.

Riemann Surfaces

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Author : Simon Donaldson
language : en
Publisher: Oxford University Press
Release Date : 2011-03-24

Riemann Surfaces written by Simon Donaldson and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-24 with Mathematics categories.

An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

Geometry Of Riemann Surfaces And Teichm Ller Spaces

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Author : M. Seppälä
language : en
Publisher: Elsevier
Release Date : 2011-08-18

Geometry Of Riemann Surfaces And Teichm Ller Spaces written by M. Seppälä and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.

The moduli problem is to describe the structure of the spaceof isomorphism classes of Riemann surfaces of a giventopological type. This space is known as the modulispace and has been at the center of pure mathematics formore than a hundred years. In spite of its age, this fieldstill attracts a lot of attention, the smooth compact Riemannsurfaces being simply complex projective algebraic curves.Therefore the moduli space of compact Riemann surfaces is alsothe moduli space of complex algebraic curves. This space lieson the intersection of many fields of mathematics and may bestudied from many different points of view.The aim of thismonograph is to present information about the structure of themoduli space using as concrete and elementary methods aspossible. This simple approach leads to a rich theory andopens a new way of treating the moduli problem, putting newlife into classical methods that were used in the study ofmoduli problems in the 1920s.

Supergeometry Super Riemann Surfaces And The Superconformal Action Functional

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Author : Enno Keßler
language : en
Publisher: Springer Nature
Release Date : 2019-08-28

Supergeometry Super Riemann Surfaces And The Superconformal Action Functional written by Enno Keßler and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-28 with Mathematics categories.

This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry. The objective is to understand its symmetries as geometric properties of super Riemann surfaces, which are particular complex super manifolds of dimension 1|1. The first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed. The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformations of the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them. This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.

Dessins D Enfants On Riemann Surfaces

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Author : Gareth A. Jones
language : en
Publisher: Springer
Release Date : 2016-03-23

Dessins D Enfants On Riemann Surfaces written by Gareth A. Jones and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-23 with Mathematics categories.

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.