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Algebraic Curves and Riemann Surfaces

1995 Mathematics
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Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 682/5 ( reviews)

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Book Synopsis Algebraic Curves and Riemann Surfaces by : Rick Miranda

Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Curves and Riemann Surfaces

1995 Mathematics
Download Algebraic Curves and Riemann Surfaces PDF Online Free

Author :
Release : 1995
Genre : Mathematics
Kind : eBook
Book Rating : 687/5 ( reviews)

GET EBOOK


Book Synopsis Algebraic Curves and Riemann Surfaces by : Rick Miranda

Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Riemann Surfaces and Algebraic Curves

2016-09-26 Mathematics
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Release : 2016-09-26
Genre : Mathematics
Kind : eBook
Book Rating : 933/5 ( reviews)

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Book Synopsis Riemann Surfaces and Algebraic Curves by : Renzo Cavalieri

Download or read book Riemann Surfaces and Algebraic Curves written by Renzo Cavalieri. This book was released on 2016-09-26. Available in PDF, EPUB and Kindle. Book excerpt: Hurwitz theory, the study of analytic functions among Riemann surfaces, is a classical field and active research area in algebraic geometry. The subject's interplay between algebra, geometry, topology and analysis is a beautiful example of the interconnectedness of mathematics. This book introduces students to this increasingly important field, covering key topics such as manifolds, monodromy representations and the Hurwitz potential. Designed for undergraduate study, this classroom-tested text includes over 100 exercises to provide motivation for the reader. Also included are short essays by guest writers on how they use Hurwitz theory in their work, which ranges from string theory to non-Archimedean geometry. Whether used in a course or as a self-contained reference for graduate students, this book will provide an exciting glimpse at mathematics beyond the standard university classes.

Complex Algebraic Curves

1992-02-20 Mathematics
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Release : 1992-02-20
Genre : Mathematics
Kind : eBook
Book Rating : 533/5 ( reviews)

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Book Synopsis Complex Algebraic Curves by : Frances Clare Kirwan

Download or read book Complex Algebraic Curves written by Frances Clare Kirwan. This book was released on 1992-02-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces

1989-01-11 Mathematics
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Release : 1989-01-11
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)

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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. This book was released on 1989-01-11. 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.

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