The Concept Of A Riemann Surface

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The Concept Of A Riemann Surface

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Author : Hermann Weyl
language : en
Publisher: Courier Corporation
Release Date : 2013-12-31

The Concept Of A Riemann Surface written by Hermann Weyl and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-31 with Mathematics categories.

This classic on the general history of functions combines function theory and geometry, forming the basis of the modern approach to analysis, geometry, and topology. 1955 edition.

Topics In The Theory Of Riemann Surfaces

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Author : Robert D.M. Accola
language : en
Publisher: Springer
Release Date : 2006-11-14

Topics In The Theory Of Riemann Surfaces written by Robert D.M. Accola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The book's main concern is automorphisms of Riemann surfaces, giving a foundational treatment from the point of view of Galois coverings, and treating the problem of the largest automorphism group for a Riemann surface of a given genus. In addition, the extent to which fixed points of automorphisms are generalized Weierstrass points is considered. The extremely useful inequality of Castelnuovo- Severi is also treated. While the methods are elementary, much of the material does not appear in the current texts on Riemann surfaces, algebraic curves. The book is accessible to a reader who has had an introductory course on the theory of Riemann surfaces or algebraic curves.

Compact Riemann Surfaces

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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

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 2013-04-17 with Mathematics categories.

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. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps.

Contributions To The Theory Of Riemann Surfaces

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Author : Lars Valerian Ahlfors
language : en
Publisher: Princeton University Press
Release Date : 1953-08-21

Contributions To The Theory Of Riemann Surfaces written by Lars Valerian Ahlfors and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953-08-21 with Mathematics categories.

The description for this book, Contributions to the Theory of Riemann Surfaces. (AM-30), Volume 30, will be forthcoming.

A First Course In String Theory

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Author : Barton Zwiebach
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-10

A First Course In String Theory written by Barton Zwiebach 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 2004-06-10 with Science categories.

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Lectures On Riemann Surfaces

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Author : Otto Forster
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Lectures On Riemann Surfaces written by Otto Forster 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 2012-12-06 with Mathematics categories.

This book grew out of lectures on Riemann surfaces which the author gave at the universities of Munich, Regensburg and Munster. Its aim is to give an introduction to this rich and beautiful subject, while presenting methods from the theory of complex manifolds which, in the special case of one complex variable, turn out to be particularly elementary and transparent. The book is divided into three chapters. In the first chapter we consider Riemann surfaces as covering spaces and develop a few basics from topology which are needed for this. Then we construct the Riemann surfaces which arise via analytic continuation of function germs. In particular this includes the Riemann surfaces of algebraic functions. As well we look more closely at analytic functions which display a special multi-valued behavior. Examples of this are the primitives of holomorphic i-forms and the solutions of linear differential equations. The second chapter is devoted to compact Riemann surfaces. The main classical results, like the Riemann-Roch Theorem, Abel's Theorem and the Jacobi inversion problem, are presented. Sheaf cohomology is an important technical tool. But only the first cohomology groups are used and these are comparatively easy to handle. The main theorems are all derived, following Serre, from the finite dimensionality of the first cohomology group with coefficients in the sheaf of holomorphic functions. And the proof of this is based on the fact that one can locally solve inhomogeneous Cauchy Riemann equations and on Schwarz' Lemma.

The Concept Of A Riemann Surface Tr

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Author : Hermann Weyl
language : en
Publisher:
Release Date :

The Concept Of A Riemann Surface Tr written by Hermann Weyl and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Riemann surfaces categories.

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.

Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces

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Author : William Mark Goldman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Rank One Higgs Bundles And Representations Of Fundamental Groups Of Riemann Surfaces written by William Mark Goldman 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 2008 with Mathematics categories.

This expository article details the theory of rank one Higgs bundles over a closed Riemann surface $X$ and their relation to representations of the fundamental group of $X$. The authors construct an equivalence between the deformation theories of flat connections and Higgs pairs. This provides an identification of moduli spaces arising in different contexts. The moduli spaces are real Lie groups. From each context arises a complex structure, and the different complex structures define a hyperkähler structure. The twistor space, real forms, and various group actions are computed explicitly in terms of the Jacobian of $X$. The authors describe the moduli spaces and their geometry in terms of the Riemann period matrix of $X$.

Riemann Surfaces

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Author : Simon Donaldson
language : en
Publisher: OUP Oxford
Release Date : 2011-03-25

Riemann Surfaces written by Simon Donaldson and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-25 with Science categories.

The theory of Riemann surfaces occupies a very special place in mathematics. It is a culmination of much of traditional calculus, making surprising connections with geometry and arithmetic. It is an extremely useful part of mathematics, knowledge of which is needed by specialists in many other fields. It provides a model for a large number of more recent developments in areas including manifold topology, global analysis, algebraic geometry, Riemannian geometry, and diverse topics in mathematical physics. This graduate text on Riemann surface theory proves the fundamental analytical results on the existence of meromorphic functions and the Uniformisation Theorem. The approach taken emphasises PDE methods, applicable more generally in global analysis. The connection with geometric topology, and in particular the role of the mapping class group, is also explained. To this end, some more sophisticated topics have been included, compared with traditional texts at this level. While the treatment is novel, the roots of the subject in traditional calculus and complex analysis are kept well in mind. Part I sets up the interplay between complex analysis and topology, with the latter treated informally. Part II works as a rapid first course in Riemann surface theory, including elliptic curves. The core of the book is contained in Part III, where the fundamental analytical results are proved. Following this section, the remainder of the text illustrates various facets of the more advanced theory.