Elementary Algebraic Geometry

Elementary Algebraic Geometry Author Klaus Hulek
ISBN-10 9780821829523
Year 2003
Pages 213
Language en
Publisher American Mathematical Soc.
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This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.

Elementary Algebraic Geometry

Elementary Algebraic Geometry Author Keith Kendig
ISBN-10 9780486801872
Year 2015-01-19
Pages 320
Language en
Publisher Courier Dover Publications
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Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring theory and algebraic geometry as well as varieties of arbitrary dimension and some elementary mathematics on curves. Upon finishing the text, students will have a foundation for advancing in several different directions, including toward a further study of complex algebraic or analytic varieties or to the scheme-theoretic treatments of algebraic geometry. 2015 edition.

Undergraduate Algebraic Geometry

Undergraduate Algebraic Geometry Author Miles Reid
ISBN-10 0521356628
Year 1988-12-15
Pages 129
Language en
Publisher Cambridge University Press
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This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.

Polyhedral and Algebraic Methods in Computational Geometry

Polyhedral and Algebraic Methods in Computational Geometry Author Michael Joswig
ISBN-10 9781447148173
Year 2013-01-04
Pages 250
Language en
Publisher Springer Science & Business Media
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Polyhedral and Algebraic Methods in Computational Geometry provides a thorough introduction into algorithmic geometry and its applications. It presents its primary topics from the viewpoints of discrete, convex and elementary algebraic geometry. The first part of the book studies classical problems and techniques that refer to polyhedral structures. The authors include a study on algorithms for computing convex hulls as well as the construction of Voronoi diagrams and Delone triangulations. The second part of the book develops the primary concepts of (non-linear) computational algebraic geometry. Here, the book looks at Gröbner bases and solving systems of polynomial equations. The theory is illustrated by applications in computer graphics, curve reconstruction and robotics. Throughout the book, interconnections between computational geometry and other disciplines (such as algebraic geometry, optimization and numerical mathematics) are established. Polyhedral and Algebraic Methods in Computational Geometry is directed towards advanced undergraduates in mathematics and computer science, as well as towards engineering students who are interested in the applications of computational geometry.

Algebraic Geometry

Algebraic Geometry Author Thomas A. Garrity
ISBN-10 9780821893968
Year 2013-02-01
Pages 335
Language en
Publisher American Mathematical Soc.
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Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of ex

Algebraic Varieties

Algebraic Varieties Author G. Kempf
ISBN-10 0521426138
Year 1993-09-09
Pages 163
Language en
Publisher Cambridge University Press
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An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

Algebraic Geometry

Algebraic Geometry Author Robin Hartshorne
ISBN-10 9781475738490
Year 2013-06-29
Pages 496
Language en
Publisher Springer Science & Business Media
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An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

Complex Algebraic Curves

Complex Algebraic Curves Author Frances Clare Kirwan
ISBN-10 0521423538
Year 1992-02-20
Pages 264
Language en
Publisher Cambridge University Press
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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.

Algebraic Geometry

Algebraic Geometry Author Joe Harris
ISBN-10 9781475721898
Year 2013-11-11
Pages 330
Language en
Publisher Springer Science & Business Media
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"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS

A Royal Road to Algebraic Geometry

A Royal Road to Algebraic Geometry Author Audun Holme
ISBN-10 3642192254
Year 2011-10-06
Pages 366
Language en
Publisher Springer Science & Business Media
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This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to read all of his work Elements. Euclid is said to have answered: “There is no royal road to geometry!” The book starts by explaining this enigmatic answer, the aim of the book being to argue that indeed, in some sense there is a royal road to algebraic geometry. From a point of departure in algebraic curves, the exposition moves on to the present shape of the field, culminating with Alexander Grothendieck’s theory of schemes. Contemporary homological tools are explained. The reader will follow a directed path leading up to the main elements of modern algebraic geometry. When the road is completed, the reader is empowered to start navigating in this immense field, and to open up the door to a wonderful field of research. The greatest scientific experience of a lifetime!

Using Algebraic Geometry

Using Algebraic Geometry Author David A Cox
ISBN-10 0387207333
Year 2005-03-17
Pages 12
Language en
Publisher Springer Science & Business Media
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The discovery of new algorithms for dealing with polynomial equations, and their implementation on fast, inexpensive computers, has revolutionized algebraic geometry and led to exciting new applications in the field. This book details many uses of algebraic geometry and highlights recent applications of Grobner bases and resultants. This edition contains two new sections, a new chapter, updated references and many minor improvements throughout.

Introduction to Commutative Algebra and Algebraic Geometry

Introduction to Commutative Algebra and Algebraic Geometry Author Ernst Kunz
ISBN-10 9781461459873
Year 2012-11-06
Pages 238
Language en
Publisher Springer Science & Business Media
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Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

Algebraic Geometry over the Complex Numbers

Algebraic Geometry over the Complex Numbers Author Donu Arapura
ISBN-10 9781461418092
Year 2012-02-15
Pages 329
Language en
Publisher Springer Science & Business Media
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This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.