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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.

Riemann Surfaces

2011-03-24 Mathematics
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Release : 2011-03-24
Genre : Mathematics
Kind : eBook
Book Rating : 393/5 ( reviews)

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Book Synopsis Riemann Surfaces by : Simon Donaldson

Download or read book Riemann Surfaces written by Simon Donaldson. This book was released on 2011-03-24. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative but accessible text on one dimensional complex manifolds or Riemann surfaces. Dealing with the main results on Riemann surfaces from a variety of points of view; it pulls together material from global analysis, topology, and algebraic geometry, and covers the essential mathematical methods and tools.

A Course in Complex Analysis and Riemann Surfaces

2014-08-06 Mathematics
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Release : 2014-08-06
Genre : Mathematics
Kind : eBook
Book Rating : 477/5 ( reviews)

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Book Synopsis A Course in Complex Analysis and Riemann Surfaces by : Wilhelm Schlag

Download or read book A Course in Complex Analysis and Riemann Surfaces written by Wilhelm Schlag. This book was released on 2014-08-06. Available in PDF, EPUB and Kindle. Book excerpt: Complex analysis is a cornerstone of mathematics, making it an essential element of any area of study in graduate mathematics. Schlag's treatment of the subject emphasizes the intuitive geometric underpinnings of elementary complex analysis that naturally lead to the theory of Riemann surfaces. The book begins with an exposition of the basic theory of holomorphic functions of one complex variable. The first two chapters constitute a fairly rapid, but comprehensive course in complex analysis. The third chapter is devoted to the study of harmonic functions on the disk and the half-plane, with an emphasis on the Dirichlet problem. Starting with the fourth chapter, the theory of Riemann surfaces is developed in some detail and with complete rigor. From the beginning, the geometric aspects are emphasized and classical topics such as elliptic functions and elliptic integrals are presented as illustrations of the abstract theory. The special role of compact Riemann surfaces is explained, and their connection with algebraic equations is established. The book concludes with three chapters devoted to three major results: the Hodge decomposition theorem, the Riemann-Roch theorem, and the uniformization theorem. These chapters present the core technical apparatus of Riemann surface theory at this level. This text is intended as a detailed, yet fast-paced intermediate introduction to those parts of the theory of one complex variable that seem most useful in other areas of mathematics, including geometric group theory, dynamics, algebraic geometry, number theory, and functional analysis. More than seventy figures serve to illustrate concepts and ideas, and the many problems at the end of each chapter give the reader ample opportunity for practice and independent study.

Geometry and Spectra of Compact Riemann Surfaces

2010-10-29 Mathematics
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Release : 2010-10-29
Genre : Mathematics
Kind : eBook
Book Rating : 921/5 ( reviews)

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Book Synopsis Geometry and Spectra of Compact Riemann Surfaces by : Peter Buser

Download or read book Geometry and Spectra of Compact Riemann Surfaces written by Peter Buser. This book was released on 2010-10-29. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a self-contained introduction to the geometry of Riemann Surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater than one, and the relationship of the Laplace operator with the geometry of such surfaces. Research workers and graduate students interested in compact Riemann surfaces will find here a number of useful tools and insights to apply to their investigations.

Lectures on Riemann Surfaces

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 614/5 ( reviews)

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Book Synopsis Lectures on Riemann Surfaces by : Otto Forster

Download or read book Lectures on Riemann Surfaces written by Otto Forster. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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

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