Algebraic Geometry Over The Complex Numbers

Author : Donu Arapura
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 51,5 Mb
Release : 2012-02-15
Category : Mathematics
ISBN : 9781461418092

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Algebraic Geometry over the Complex Numbers by Donu Arapura Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 344 pages
File Size : 52,7 Mb
Release : 2012-02-16
Category : Electronic
ISBN : 1461418100

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Algebraic Geometry Over the Complex Numbers by Anonim Pdf

Author : I. M. Yaglom
Publisher : Academic Press
Page : 256 pages
File Size : 40,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483266633

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Complex Numbers in Geometry by I. M. Yaglom Pdf

Complex Numbers in Geometry focuses on the principles, interrelations, and applications of geometry and algebra. The book first offers information on the types and geometrical interpretation of complex numbers. Topics include interpretation of ordinary complex numbers in the Lobachevskii plane; double numbers as oriented lines of the Lobachevskii plane; dual numbers as oriented lines of a plane; most general complex numbers; and double, hypercomplex, and dual numbers. The text then takes a look at circular transformations and circular geometry, including ordinary circular transformations, axial circular transformations of the Lobachevskii plane, circular transformations of the Lobachevskii plane, axial circular transformations, and ordinary circular transformations. The manuscript is intended for pupils in high schools and students in the mathematics departments of universities and teachers' colleges. The publication is also useful in the work of mathematical societies and teachers of mathematics in junior high and high schools.

Author : Nolan R. Wallach
Publisher : Springer
Page : 190 pages
File Size : 45,9 Mb
Release : 2017-09-08
Category : Mathematics
ISBN : 9783319659077

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Geometric Invariant Theory by Nolan R. Wallach Pdf

Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. This sophisticated topic is elegantly presented with enough background theory included to make the text accessible to advanced graduate students in mathematics and physics with diverse backgrounds in algebraic and differential geometry. Throughout the book, examples are emphasized. Exercises add to the reader’s understanding of the material; most are enhanced with hints. The exposition is divided into two parts. The first part, ‘Background Theory’, is organized as a reference for the rest of the book. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature. Chapter 1 emphasizes the relationship between the Zariski topology and the canonical Hausdorff topology of an algebraic variety over the complex numbers. Chapter 2 develops the interaction between Lie groups and algebraic groups. Part 2, ‘Geometric Invariant Theory’ consists of three chapters (3–5). Chapter 3 centers on the Hilbert–Mumford theorem and contains a complete development of the Kempf–Ness theorem and Vindberg’s theory. Chapter 4 studies the orbit structure of a reductive algebraic group on a projective variety emphasizing Kostant’s theory. The final chapter studies the extension of classical invariant theory to products of classical groups emphasizing recent applications of the theory to physics.

Author : Hans Schwerdtfeger
Publisher : Courier Corporation
Page : 224 pages
File Size : 40,8 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486135861

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Geometry of Complex Numbers by Hans Schwerdtfeger Pdf

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Author : Rick Miranda
Publisher : American Mathematical Soc.
Page : 390 pages
File Size : 45,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821802687

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Algebraic Curves and Riemann Surfaces by Rick Miranda Pdf

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.

Author : Kenji Ueno
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 48,6 Mb
Release : 1997
Category : Mathematics
ISBN : 9780821811443

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An Introduction to Algebraic Geometry by Kenji Ueno Pdf

This introduction to algebraic geometry allows readers to grasp the fundamentals of the subject with only linear algebra and calculus as prerequisites. After a brief history of the subject, the book introduces projective spaces and projective varieties, and explains plane curves and resolution of their singularities. The volume further develops the geometry of algebraic curves and treats congruence zeta functions of algebraic curves over a finite field. It concludes with a complex analytical discussion of algebraic curves. The author emphasizes computation of concrete examples rather than proofs, and these examples are discussed from various viewpoints. This approach allows readers to develop a deeper understanding of the theorems.

Author : Herbert Lange
Publisher : Unknown
Page : 0 pages
File Size : 43,9 Mb
Release : 2023
Category : Electronic
ISBN : 3031255712

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Abelian Varieties Over the Complex Numbers by Herbert Lange Pdf

This textbook offers an introduction to abelian varieties, a rich topic of central importance to algebraic geometry. The emphasis is on geometric constructions over the complex numbers, notably the construction of important classes of abelian varieties and their algebraic cycles. The book begins with complex tori and their line bundles (theta functions), naturally leading to the definition of abelian varieties. After establishing basic properties, the moduli space of abelian varieties is introduced and studied. The next chapters are devoted to the study of the main examples of abelian varieties: Jacobian varieties, abelian surfaces, Albanese and Picard varieties, Prym varieties, and intermediate Jacobians. Subsequently, the Fourier-Mukai transform is introduced and applied to the study of sheaves, and results on Chow groups and the Hodge conjecture are obtained. This book is suitable for use as the main text for a first course on abelian varieties, for instance as a second graduate course in algebraic geometry. The variety of topics and abundant exercises also make it well suited to reading courses. The book provides an accessible reference, not only for students specializing in algebraic geometry but also in related subjects such as number theory, cryptography, mathematical physics, and integrable systems.

Author : Roland Deaux
Publisher : Courier Corporation
Page : 211 pages
File Size : 45,7 Mb
Release : 2008-03-05
Category : Mathematics
ISBN : 9780486466293

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Introduction to the Geometry of Complex Numbers by Roland Deaux Pdf

Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.

Author : Titu Andreescu,Dorin Andrica
Publisher : Springer Science & Business Media
Page : 336 pages
File Size : 46,5 Mb
Release : 2007-10-08
Category : Mathematics
ISBN : 9780817644499

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Complex Numbers from A to ...Z by Titu Andreescu,Dorin Andrica Pdf

* Learn how complex numbers may be used to solve algebraic equations, as well as their geometric interpretation * Theoretical aspects are augmented with rich exercises and problems at various levels of difficulty * A special feature is a selection of outstanding Olympiad problems solved by employing the methods presented * May serve as an engaging supplemental text for an introductory undergrad course on complex numbers or number theory

Author : W.E. Jenner
Publisher : Courier Dover Publications
Page : 115 pages
File Size : 43,6 Mb
Release : 2018-01-16
Category : Mathematics
ISBN : 9780486818061

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Rudiments of Algebraic Geometry by W.E. Jenner Pdf

Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 44,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475738490

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Algebraic Geometry by Robin Hartshorne Pdf

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.

Author : Liang-shin Hahn
Publisher : Cambridge University Press
Page : 212 pages
File Size : 54,6 Mb
Release : 1994
Category : Mathematics
ISBN : 0883855100

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Complex Numbers and Geometry by Liang-shin Hahn Pdf

This book demonstrates how complex numbers and geometry can be blended together to give easy proofs of many theorems in plane geometry.

Author : Claire Voisin
Publisher : Cambridge University Press
Page : 334 pages
File Size : 42,7 Mb
Release : 2007-12-20
Category : Mathematics
ISBN : 0521718015

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Hodge Theory and Complex Algebraic Geometry I: by Claire Voisin Pdf

This is a modern introduction to Kaehlerian geometry and Hodge structure. Coverage begins with variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory (with the latter being treated in a more theoretical way than is usual in geometry). The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions.

Author : W. V. D. Hodge,Daniel Pedoe
Publisher : CUP Archive
Page : 452 pages
File Size : 54,7 Mb
Release : 2024-06-10
Category : Geometry, Algebraic
ISBN : 8210379456XXX

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Methods of Algebraic Geometry by W. V. D. Hodge,Daniel Pedoe Pdf