Compact Riemann Surfaces And Algebraic Curves

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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.

Compact Riemann Surfaces And Algebraic Curves

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Author : Kichoon Yang
language : en
Publisher: World Scientific
Release Date : 1988

Compact Riemann Surfaces And Algebraic Curves written by Kichoon Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

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.

Symmetries Of Compact Riemann Surfaces

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Author : Emilio Bujalance
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-06

Symmetries Of Compact Riemann Surfaces written by Emilio Bujalance 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 2010-10-06 with Mathematics categories.

This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.

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.

Compact Riemann Surfaces

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Author : R. Narasimhan
language : en
Publisher: Springer Science & Business Media
Release Date : 1992-09-01

Compact Riemann Surfaces written by R. Narasimhan 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 1992-09-01 with Mathematics categories.

The lecture notes forming a course given by the author at the Eidgenossische Technische Hochschule, Zurich, from November 1984 to February 1985. Presents the basic theorems about the Jacobian from Riemann's own point of view. Annotation copyrighted by Book News, Inc., Portland, OR

Complex Algebraic Curves

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Author : Frances Clare Kirwan
language : en
Publisher: Cambridge University Press
Release Date : 1992-02-20

Complex Algebraic Curves written by Frances Clare Kirwan 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 1992-02-20 with Mathematics categories.

This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

Introduction To Compact Riemann Surfaces And Dessins D Enfants

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Author : Ernesto Girondo
language : en
Publisher: Cambridge University Press
Release Date : 2012

Introduction To Compact Riemann Surfaces And Dessins D Enfants written by Ernesto Girondo 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 2012 with Mathematics categories.

An elementary account of the theory of compact Riemann surfaces and an introduction to the Belyi-Grothendieck theory of dessins d'enfants.

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.

Algebraic Geometry I

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Author : V.I. Danilov
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-03-17

Algebraic Geometry I written by V.I. Danilov 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 1998-03-17 with Mathematics categories.

"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum

Dessins D Enfants On Riemann Surfaces

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Author : Gareth A. Jones
language : en
Publisher: Springer
Release Date : 2018-04-19

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 2018-04-19 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.