Algebraic Curves And Riemann Surfaces


Algebraic Curves And Riemann Surfaces
Author: Rick Miranda
Publisher: American Mathematical Soc.
ISBN: 0821802682
Size: 75.84 MB
Format: PDF
View: 7018
Get Books

Algebraic Curves And Riemann Surfaces

eBook File: Algebraic-curves-and-riemann-surfaces.PDF Book by Rick Miranda, Algebraic Curves And Riemann Surfaces Books available in PDF, EPUB, Mobi Format. Download Algebraic Curves And Riemann Surfaces books, 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.


Algebraic Curves and Riemann Surfaces
Language: en
Pages: 390
Authors: Rick Miranda
Categories: Mathematics
Type: BOOK - Published: 1995 - Publisher: American Mathematical Soc.
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
Moduli of Riemann Surfaces, Real Algebraic Curves, and Their Superanalogs
Language: en
Pages:
Authors: S. M. Natanzon
Categories: Mathematics
Type: BOOK - Published: - Publisher: American Mathematical Soc.
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. The present book is devoted to the study of topological properties of this space and of similar moduli spaces, such as the space of real algebraic
Complex Algebraic Curves
Language: en
Pages: 264
Authors: Frances Clare Kirwan, Frances Kirwan
Categories: Mathematics
Type: BOOK - Published: 1992-02-20 - Publisher: Cambridge University Press
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
Principles of Algebraic Geometry
Language: en
Pages: 832
Authors: Phillip Griffiths, Joseph Harris
Categories: Mathematics
Type: BOOK - Published: 2014-08-21 - Publisher: John Wiley & Sons
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold
A First Course in Modular Forms
Language: en
Pages: 450
Authors: Fred Diamond, Jerry Shurman
Categories: Mathematics
Type: BOOK - Published: 2006-03-30 - Publisher: Springer Science & Business Media
This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and
An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
Language: en
Pages: 217
Authors: Martin Schlichenmaier
Categories: Science
Type: BOOK - Published: 2010-02-11 - Publisher: Springer Science & Business Media
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
Introduction to Algebraic Curves
Language: en
Pages: 225
Authors: Phillip A. Griffiths
Categories: Mathematics
Type: BOOK - Published: 1989 - Publisher: American Mathematical Soc.
This book differs from a number of recent books on this subject in that it combines analytic and geometric methods at the outset, so that the reader can grasp the basic results of the subject. Although such modern techniques of sheaf theory, cohomology, and commutative algebra are not covered here,
Bulletin of the American Mathematical Society
Language: en
Pages:
Authors: American Mathematical Society
Categories: Mathematics
Type: BOOK - Published: 1894 - Publisher:
Books about Bulletin of the American Mathematical Society
Bulletin (new Series) of the American Mathematical Society
Language: en
Pages:
Authors: American Mathematical Society
Categories: Mathematics
Type: BOOK - Published: 1894 - Publisher:
Books about Bulletin (new Series) of the American Mathematical Society
Bulletin of the New York Mathematical Society
Language: en
Pages:
Authors: American Mathematical Society
Categories: Mathematics
Type: BOOK - Published: 1894 - Publisher:
Books about Bulletin of the New York Mathematical Society