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An Introduction To Riemann Surfaces Algebraic Curves And Moduli Spaces
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Book Synopsis An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces by : Martin Schlichenmaier
Download or read book An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces written by Martin Schlichenmaier and published by Springer Science & Business Media. This book was released on 2010-02-11 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces by : Martin Schlichenmaier
Download or read book An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces written by Martin Schlichenmaier and published by Springer. This book was released on 2014-10-09 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Moduli Spaces of Riemann Surfaces by : Benson Farb
Download or read book Moduli Spaces of Riemann Surfaces written by Benson Farb and published by American Mathematical Soc.. This book was released on 2013-08-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs by : S. M. Natanzon
Download or read book Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs written by S. M. Natanzon and published by American Mathematical Soc.. This book was released on with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves by : Lizhen Ji
Download or read book Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves written by Lizhen Ji and published by . This book was released on 2017-12-30 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Geometry of Riemann Surfaces and Teichmüller Spaces by : M. Seppälä
Download or read book Geometry of Riemann Surfaces and Teichmüller Spaces written by M. Seppälä and published by Elsevier. This book was released on 2011-08-18 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moduli problem is to describe the structure of the space of isomorphism classes of Riemann surfaces of a given topological type. This space is known as the moduli space and has been at the center of pure mathematics for more than a hundred years. In spite of its age, this field still attracts a lot of attention, the smooth compact Riemann surfaces being simply complex projective algebraic curves. Therefore the moduli space of compact Riemann surfaces is also the moduli space of complex algebraic curves. This space lies on the intersection of many fields of mathematics and may be studied from many different points of view. The aim of this monograph is to present information about the structure of the moduli space using as concrete and elementary methods as possible. This simple approach leads to a rich theory and opens a new way of treating the moduli problem, putting new life into classical methods that were used in the study of moduli problems in the 1920s.
Book Synopsis Riemann Surfaces and Algebraic Curves by : Renzo Cavalieri
Download or read book Riemann Surfaces and Algebraic Curves written by Renzo Cavalieri and published by Cambridge University Press. This book was released on 2016-09-26 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.
Book Synopsis Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves by : Lizhen Ji
Download or read book Introduction to Moduli Spaces of Riemann Surfaces and Tropical Curves written by Lizhen Ji and published by . This book was released on 2017 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Curves by : Maxim E. Kazaryan
Download or read book Algebraic Curves written by Maxim E. Kazaryan and published by Springer. This book was released on 2019-01-21 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a concise yet thorough introduction to the notion of moduli spaces of complex algebraic curves. Over the last few decades, this notion has become central not only in algebraic geometry, but in mathematical physics, including string theory, as well. The book begins by studying individual smooth algebraic curves, including the most beautiful ones, before addressing families of curves. Studying families of algebraic curves often proves to be more efficient than studying individual curves: these families and their total spaces can still be smooth, even if there are singular curves among their members. A major discovery of the 20th century, attributed to P. Deligne and D. Mumford, was that curves with only mild singularities form smooth compact moduli spaces. An unexpected byproduct of this discovery was the realization that the analysis of more complex curve singularities is not a necessary step in understanding the geometry of the moduli spaces. The book does not use the sophisticated machinery of modern algebraic geometry, and most classical objects related to curves – such as Jacobian, space of holomorphic differentials, the Riemann-Roch theorem, and Weierstrass points – are treated at a basic level that does not require a profound command of algebraic geometry, but which is sufficient for extending them to vector bundles and other geometric objects associated to moduli spaces. Nevertheless, it offers clear information on the construction of the moduli spaces, and provides readers with tools for practical operations with this notion. Based on several lecture courses given by the authors at the Independent University of Moscow and Higher School of Economics, the book also includes a wealth of problems, making it suitable not only for individual research, but also as a textbook for undergraduate and graduate coursework
Book Synopsis Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces by : Maurizio Cornalba
Download or read book Lectures On Riemann Surfaces - Proceedings Of The College On Riemann Surfaces written by Maurizio Cornalba and published by World Scientific. This book was released on 1989-06-01 with total page 716 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Algebraic Curves and Riemann Surfaces by : Rick Miranda
Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda and published by American Mathematical Soc.. This book was released on 1995 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book was easy to understand, with many examples. The exercises were well chosen, and served to give further examples and developments of the theory. --William Goldman, University of Maryland 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 center stage. But the main examples come from projective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Duality 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 and cohomology are introduced as a unifying device in the latter chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one semester of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-semester course in complex variables or a year-long course in algebraic geometry.
Book Synopsis Mapping Class Groups and Moduli Spaces of Riemann Surfaces by : Carl-Friedrich Bödigheimer
Download or read book Mapping Class Groups and Moduli Spaces of Riemann Surfaces written by Carl-Friedrich Bödigheimer and published by American Mathematical Soc.. This book was released on 1993 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of mapping class groups and moduli spaces of compact Riemann surfaces is currently a central topic in topology, algebraic geometry, and conformal field theory. This book contains proceedings from two workshops held in the summer of 1991, one at the University of G\ottingen and the other at the University of Washington at Seattle. The papers gathered here represent diverse approaches and contain several important new results. With both research and survey articles, the book appeals to mathematicians and physicists.
Book Synopsis Compact Riemann Surfaces and Algebraic Curves by : Kichoon Yang
Download or read book Compact Riemann Surfaces and Algebraic Curves written by Kichoon Yang and published by World Scientific. This book was released on 1988-11-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:Topological Preliminaries —Singular Homology and Relative HomologyCellular HomologyDe Rham CohomologyCommutative Algebra — An Introduction —Closed Ideals and VarietiesCoordinate RingsDimension TheoryIntersection NumbersSingular Plane Curves —The Classical Plücker FormulaeDivisors on a Compact Complex Manifold —Divisors and Holomorphic Line BundlesLinear Systems on a Compact Riemann Surface and Holomorphic MapsCompact Riemann Surfaces —The Jacobian Variety and Abel's TheoremThe Riemann-Roch Theorem and the Canonical EmbeddingHyperelliptic Riemann Surfaces and the Weierstrass PointsGeometry of Projective Curves — The Complex Flag ManifoldMetric Geometry of Projective CurvesPlücker Formulae for Projective Algebraic CurvesHarmonic Maps from a Compact Riemann SurfaceA Brief Look at Algebraic Surfaces —The Intersection FormBlow-Ups and Rational MapsThe Kodaira Dimension of an Algebraic Surface Readership: Mathematicians. Keywords:Compact Riemann Surfaces;Algebraic Curves;Compact Complex Manifold;Algebraic Surfaces
Book Synopsis Algebraic Curves and Riemann Surfaces for Undergraduates by : Anil Nerode
Download or read book Algebraic Curves and Riemann Surfaces for Undergraduates written by Anil Nerode and published by Springer Nature. This book was released on 2023-01-16 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory relating algebraic curves and Riemann surfaces exhibits the unity of mathematics: topology, complex analysis, algebra and geometry all interact in a deep way. This textbook offers an elementary introduction to this beautiful theory for an undergraduate audience. At the heart of the subject is the theory of elliptic functions and elliptic curves. A complex torus (or “donut”) is both an abelian group and a Riemann surface. It is obtained by identifying points on the complex plane. At the same time, it can be viewed as a complex algebraic curve, with addition of points given by a geometric “chord-and-tangent” method. This book carefully develops all of the tools necessary to make sense of this isomorphism. The exposition is kept as elementary as possible and frequently draws on familiar notions in calculus and algebra to motivate new concepts. Based on a capstone course given to senior undergraduates, this book is intended as a textbook for courses at this level and includes a large number of class-tested exercises. The prerequisites for using the book are familiarity with abstract algebra, calculus and analysis, as covered in standard undergraduate courses.
Book Synopsis The Moduli Space of Curves by : Robert H. Dijkgraaf
Download or read book The Moduli Space of Curves written by Robert H. Dijkgraaf and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: The moduli space Mg of curves of fixed genus g – that is, the algebraic variety that parametrizes all curves of genus g – is one of the most intriguing objects of study in algebraic geometry these days. Its appeal results not only from its beautiful mathematical structure but also from recent developments in theoretical physics, in particular in conformal field theory.
Author :Thiruvalloor E. Venkata Balaji Publisher :Universitätsverlag Göttingen ISBN 13 :3941875329 Total Pages :241 pages Book Rating :4.9/5 (418 download)
Book Synopsis An Introduction to Families, Deformations and Moduli by : Thiruvalloor E. Venkata Balaji
Download or read book An Introduction to Families, Deformations and Moduli written by Thiruvalloor E. Venkata Balaji and published by Universitätsverlag Göttingen. This book was released on 2010 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Moduli Theory is one of those areas of Mathematics that has fascinated minds from classical to modern times. This has been so because it reveals beautiful Geometry naturally hidden in questions involving classification of geometric objects and because of the profound use of the methods of several areas of Mathematics like Algebra, Number Theory, Topology and Analysis to achieve this revelation. A study of Moduli Theory would therefore give senior undergraduate and graduate students an integrated view of Mathematics. The present book is a humble introduction to some aspects of Moduli Theory.
Book Synopsis Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces by : Milagros Izquierdo
Download or read book Riemann and Klein Surfaces, Automorphisms, Symmetries and Moduli Spaces written by Milagros Izquierdo and published by American Mathematical Soc.. This book was released on 2014-11-21 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Riemann and Klein Surfaces, Symmetries and Moduli Spaces, in honor of Emilio Bujalance, held from June 24-28, 2013, at Linköping University. The conference and this volume are devoted to the mathematics that Emilio Bujalance has worked with in the following areas, all with a computational flavor: Riemann and Klein surfaces, automorphisms of real and complex surfaces, group actions on surfaces and topological properties of moduli spaces of complex curves and Abelian varieties.
