An Introduction To Riemann Surfaces Algebraic Curves And Moduli Spaces
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| Author | : Martin Schlichenmaier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2010-02-11 |
| Genre | : Science |
| ISBN | : 3540711759 |
Download An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces Book in PDF, Epub and Kindle
This book gives an introduction to modern geometry. Starting from an elementary level, the author develops deep geometrical concepts that play an important role in contemporary theoretical physics, presenting various techniques and viewpoints along the way. This second edition contains two additional, more advanced geometric techniques: the modern language and modern view of Algebraic Geometry and Mirror Symmetry.
| Author | : Martin Schlichenmaier |
| Publisher | : Springer |
| Total Pages | : 172 |
| Release | : 1989-01-11 |
| Genre | : Mathematics |
| ISBN | : |
Download An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces Book in PDF, Epub and Kindle
This lecture is intended as an introduction to the mathematical concepts of algebraic and analytic geometry. It is addressed primarily to theoretical physicists, in particular those working in string theories. The author gives a very clear exposition of the main theorems, introducing the necessary concepts by lucid examples, and shows how to work with the methods of algebraic geometry. As an example he presents the Krichever-Novikov construction of algebras of Virasaro type. The book will be welcomed by many researchers as an overview of an important branch of mathematics, a collection of useful formulae and an excellent guide to the more extensive mathematical literature.
| Author | : Benson Farb |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 371 |
| Release | : 2013-08-16 |
| Genre | : Mathematics |
| ISBN | : 0821898876 |
Download Moduli Spaces of Riemann Surfaces Book in PDF, Epub and Kindle
Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
| Author | : Lizhen Ji |
| Publisher | : |
| Total Pages | : 232 |
| Release | : 2017-12-30 |
| Genre | : Geometry, Algebraic |
| ISBN | : 9781571463531 |
Download Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves Book in PDF, Epub and Kindle
The concept of Riemann surfaces was introduced in Riemann's thesis, and the moduli space of Riemann surfaces was defined by Riemann in a masterpiece a few years later. Due to a broad connection with many subjects in mathematics and physics, Riemann surfaces and their moduli spaces have been intensively studied and should continue to attract attention in years to come. Recently, there has been an explosion of interest in and work on tropical algebraic curves--analogues of algebraic curves over the complex numbers and hence of Riemann surfaces. This book is an accessible introduction to all these topics, with special emphasis given to their many connections with subjects such as algebraic geometry, complex analysis, hyperbolic geometry, topology, geometric group theory, and mathematical physics.
| Author | : S. M. Natanzon |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 172 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : 9780821889657 |
Download Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs Book in PDF, Epub and Kindle
The space of all Riemann surfaces (the so-called moduli space) plays an important role in algebraic geometry and its applications to quantum field theory. This book focuses on the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic curves, and the space of mappings.
| Author | : M. Seppälä |
| Publisher | : Elsevier |
| Total Pages | : 269 |
| Release | : 2011-08-18 |
| Genre | : Mathematics |
| ISBN | : 0080872808 |
Download Geometry of Riemann Surfaces and Teichmüller Spaces Book in PDF, Epub and Kindle
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.
| Author | : Renzo Cavalieri |
| Publisher | : Cambridge University Press |
| Total Pages | : 197 |
| Release | : 2016-09-26 |
| Genre | : Mathematics |
| ISBN | : 110714924X |
Download Riemann Surfaces and Algebraic Curves Book in PDF, Epub and Kindle
Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.
| Author | : Kichoon Yang |
| Publisher | : World Scientific |
| Total Pages | : 184 |
| Release | : 1988-11-01 |
| Genre | : Mathematics |
| ISBN | : 9814520039 |
Download Compact Riemann Surfaces And Algebraic Curves Book in PDF, Epub and Kindle
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.
| Author | : Maurizio Cornalba |
| Publisher | : World Scientific |
| Total Pages | : 716 |
| Release | : 1989-06-01 |
| Genre | : Mathematics |
| ISBN | : 9814590878 |
Download Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces Book in PDF, Epub and Kindle
| Author | : Rick Miranda |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 414 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821802682 |
Download Algebraic Curves and Riemann Surfaces Book in PDF, Epub and Kindle
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.
