Compact Riemann Surfaces And Algebraic Curves

Author : Rick Miranda
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 45,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821802687

Get Book

Algebraic Curves and Riemann Surfaces by Rick Miranda Pdf

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.

Author : Kichoon Yang
Publisher : World Scientific
Page : 184 pages
File Size : 52,7 Mb
Release : 1988-11-01
Category : Mathematics
ISBN : 9789814520034

Get Book

Compact Riemann Surfaces and Algebraic Curves by Kichoon Yang Pdf

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

Author : Ernesto Girondo,Gabino González-Diez
Publisher : Cambridge University Press
Page : 311 pages
File Size : 40,8 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9781139504188

Get Book

Introduction to Compact Riemann Surfaces and Dessins d’Enfants by Ernesto Girondo,Gabino González-Diez Pdf

Few books on the subject of Riemann surfaces cover the relatively modern theory of dessins d'enfants (children's drawings), which was launched by Grothendieck in the 1980s and is now an active field of research. In this 2011 book, the authors begin with an elementary account of the theory of compact Riemann surfaces viewed as algebraic curves and as quotients of the hyperbolic plane by the action of Fuchsian groups of finite type. They then use this knowledge to introduce the reader to the theory of dessins d'enfants and its connection with algebraic curves defined over number fields. A large number of worked examples are provided to aid understanding, so no experience beyond the undergraduate level is required. Readers without any previous knowledge of the field of dessins d'enfants are taken rapidly to the forefront of current research.

Author : Emilio Bujalance,Emilio Bujalance García,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 49,8 Mb
Release : 2010-10-06
Category : Mathematics
ISBN : 9783642148279

Get Book

Symmetries of Compact Riemann Surfaces by Emilio Bujalance,Emilio Bujalance García,Francisco Javier Cirre,José Manuel Gamboa,Grzegorz Gromadzki Pdf

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.

Author : R. Narasimhan
Publisher : Birkhäuser
Page : 127 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034886178

Get Book

Compact Riemann Surfaces by R. Narasimhan Pdf

Author : Frances Clare Kirwan
Publisher : Cambridge University Press
Page : 278 pages
File Size : 50,5 Mb
Release : 1992-02-20
Category : Mathematics
ISBN : 0521423538

Get Book

Complex Algebraic Curves by Frances Clare Kirwan Pdf

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.

Author : Ernesto Girondo,Gabino González-Diez
Publisher : Cambridge University Press
Page : 311 pages
File Size : 45,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9780521519632

Get Book

Introduction to Compact Riemann Surfaces and Dessins D'Enfants by Ernesto Girondo,Gabino González-Diez Pdf

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

Author : V.I. Danilov,V.V. Shokurov
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 43,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642578786

Get Book

Algebraic Geometry I by V.I. Danilov,V.V. Shokurov Pdf

"... 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

Author : S. M. Natanzon
Publisher : American Mathematical Soc.
Page : 172 pages
File Size : 43,9 Mb
Release : 2024-06-28
Category : Mathematics
ISBN : 0821889656

Get Book

Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs by S. M. Natanzon Pdf

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 : Martin Schlichenmaier
Publisher : Springer
Page : 149 pages
File Size : 53,9 Mb
Release : 2014-10-09
Category : Mathematics
ISBN : 3662137283

Get Book

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces by Martin Schlichenmaier Pdf

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 : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 304 pages
File Size : 47,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662034460

Get Book

Compact Riemann Surfaces by Jürgen Jost Pdf

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.

Author : Robert D.M. Accola
Publisher : Springer
Page : 117 pages
File Size : 47,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540490562

Get Book

Topics in the Theory of Riemann Surfaces by Robert D.M. Accola Pdf

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.

Author : Renzo Cavalieri,Eric Miles
Publisher : Cambridge University Press
Page : 197 pages
File Size : 49,8 Mb
Release : 2016-09-26
Category : Mathematics
ISBN : 9781107149243

Get Book

Riemann Surfaces and Algebraic Curves by Renzo Cavalieri,Eric Miles Pdf

Classroom-tested and featuring over 100 exercises, this text introduces the key algebraic geometry field of Hurwitz theory.

Author : Otto Forster
Publisher : Springer Science & Business Media
Page : 262 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461259619

Get Book

Lectures on Riemann Surfaces by Otto Forster Pdf

This book grew out of lectures on Riemann surfaces given by Otto Forster at the universities of Munich, Regensburg, and Münster. It provides a concise modern introduction to this rewarding subject, as well as presenting methods used in the study of complex manifolds in the special case of complex dimension one. From the reviews: "This book deserves very serious consideration as a text for anyone contemplating giving a course on Riemann surfaces."—-MATHEMATICAL REVIEWS

Author : M. Seppälä,T. Sorvali
Publisher : Elsevier
Page : 262 pages
File Size : 49,9 Mb
Release : 2011-08-18
Category : Mathematics
ISBN : 0080872808

Get Book

Geometry of Riemann Surfaces and Teichmüller Spaces by M. Seppälä,T. Sorvali Pdf

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.