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Complex Algebraic Curves

Complex Algebraic Curves
Author: Frances Clare Kirwan
Publisher: Cambridge University Press
ISBN: 9780521423533
Size: 39.36 MB
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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.
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 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.
Algebraic Curves
Language: en
Pages: 231
Authors: Maxim E. Kazaryan, Sergei K. Lando, Victor V. Prasolov
Categories: Mathematics
Type: BOOK - Published: 2019-01-21 - Publisher: Springer
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
Algebraic Curves, the Brill and Noether Way
Language: en
Pages: 224
Authors: Eduardo Casas-Alvero
Categories: Mathematics
Type: BOOK - Published: 2019-11-30 - Publisher: Springer Nature
The book presents the central facts of the local, projective and intrinsic theories of complex algebraic plane curves, with complete proofs and starting from low-level prerequisites. It includes Puiseux series, branches, intersection multiplicity, Bézout theorem, rational functions, Riemann-Roch theorem and rational maps. It is aimed at graduate and advanced undergraduate students, and also at anyone interested in algebraic curves or in an introduction to algebraic geometry via curves.
Algebraic Geometry I
Language: en
Pages: 310
Authors: V.I. Danilov, V.V. Shokurov
Categories: Mathematics
Type: BOOK - Published: 1998-03-17 - Publisher: Springer Science & Business Media
"... 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
Algebraic Geometry III
Language: en
Pages: 270
Authors: A.N. Parshin, I.R. Shafarevich
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media
This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.
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 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
Algebraic Geometry I
Language: en
Pages: 310
Authors: V.I. Danilov, V.V. Shokurov
Categories: Mathematics
Type: BOOK - Published: 2013-12-01 - Publisher: Springer Science & Business Media
"... 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
Complex Algebraic Curves China Edition
Language: en
Pages: 264
Authors: Frances Kirwan
Categories: Curves, Algebraic
Type: BOOK - Published: 1992 - Publisher:
Books about Complex Algebraic Curves China Edition
Algebraic Geometry III
Language: en
Pages: 270
Authors: A.N. Parshin, I.R. Shafarevich
Categories: Mathematics
Type: BOOK - Published: 2014-03-12 - Publisher: Springer
This two-part EMS volume provides a succinct summary of complex algebraic geometry, coupled with a lucid introduction to the recent work on the interactions between the classical area of the geometry of complex algebraic curves and their Jacobian varieties. An excellent companion to the older classics on the subject.
Ebene algebraische Kurven
Language: de
Pages: 964
Authors: Egbert Brieskorn, Horst Knörrer
Categories: Courbes algébriques
Type: BOOK - Published: 1981 - Publisher:
Books about Ebene algebraische Kurven