Computational Approach To The Geometry Of Compact Riemann Surfaces
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Computational Approach To The Geometry Of Compact Riemann Surfaces
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Author : Manuel Racle
language : en
Publisher:
Release Date : 2013
Computational Approach To The Geometry Of Compact Riemann Surfaces written by Manuel Racle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
Computational Approach To Riemann Surfaces
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Author : Alexander I. Bobenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-12
Computational Approach To Riemann Surfaces written by Alexander I. Bobenko 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 2011-02-12 with Mathematics categories.
This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surface theory are presented. The intended audience of this book is twofold. It can be used as a textbook for a graduate course in numerics of Riemann surfaces, in which case the standard undergraduate background, i.e., calculus and linear algebra, is required. In particular, no knowledge of the theory of Riemann surfaces is expected; the necessary background in this theory is contained in the Introduction chapter. At the same time, this book is also intended for specialists in geometry and mathematical physics applying the theory of Riemann surfaces in their research. It is the first book on numerics of Riemann surfaces that reflects the progress made in this field during the last decade, and it contains original results. There are a growing number of applications that involve the evaluation of concrete characteristics of models analytically described in terms of Riemann surfaces. Many problem settings and computations in this volume are motivated by such concrete applications in geometry and mathematical physics.
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.
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.
Modular Forms A Computational Approach
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Author : William A. Stein
language : en
Publisher: American Mathematical Soc.
Release Date : 2007-02-13
Modular Forms A Computational Approach written by William A. Stein 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 2007-02-13 with Mathematics categories.
This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.
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.
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.
Geometry Mechanics And Dynamics
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Author : Dong Eui Chang
language : en
Publisher: Springer
Release Date : 2015-04-16
Geometry Mechanics And Dynamics written by Dong Eui Chang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-16 with Mathematics categories.
This book illustrates the broad range of Jerry Marsden’s mathematical legacy in areas of geometry, mechanics, and dynamics, from very pure mathematics to very applied, but always with a geometric perspective. Each contribution develops its material from the viewpoint of geometric mechanics beginning at the very foundations, introducing readers to modern issues via illustrations in a wide range of topics. The twenty refereed papers contained in this volume are based on lectures and research performed during the month of July 2012 at the Fields Institute for Research in Mathematical Sciences, in a program in honor of Marsden's legacy. The unified treatment of the wide breadth of topics treated in this book will be of interest to both experts and novices in geometric mechanics. Experts will recognize applications of their own familiar concepts and methods in a wide variety of fields, some of which they may never have approached from a geometric viewpoint. Novices may choose topics that interest them among the various fields and learn about geometric approaches and perspectives toward those topics that will be new for them as well.
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.
An Introduction To Algebraic Geometry
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Author : Frank-Olaf Schreyer
language : en
Publisher: Springer Nature
Release Date : 2025-04-30
An Introduction To Algebraic Geometry written by Frank-Olaf Schreyer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-30 with Mathematics categories.
Algebraic Geometry is a huge area of mathematics which went through several phases: Hilbert's fundamental paper from 1890, sheaves and cohomology introduced by Serre in the 1950s, Grothendieck's theory of schemes in the 1960s and so on. This book covers the basic material known before Serre's introduction of sheaves to the subject with an emphasis on computational methods. In particular, we will use Gröbner basis systematically. The highlights are the Nullstellensatz, Gröbner basis, Hilbert's syzygy theorem and the Hilbert function, Bézout’s theorem, semi-continuity of the fiber dimension, Bertini's theorem, Cremona resolution of plane curves and parametrization of rational curves. In the final chapter we discuss the proof of the Riemann-Roch theorem due to Brill and Noether, and give its basic applications.The algorithm to compute the Riemann-Roch space of a divisor on a curve, which has a plane model with only ordinary singularities, use adjoint systems. The proof of the completeness of adjoint systems becomes much more transparent if one use cohomology of coherent sheaves. Instead of giving the original proof of Max Noether, we explain in an appendix how this easily follows from standard facts on cohomology of coherent sheaves. The book aims at undergraduate students. It could be a course book for a first Algebraic Geometry lecture, and hopefully motivates further studies.