An Introduction To Algebraic Geometry

Author : Steven Dale Cutkosky
Publisher : American Mathematical Soc.
Page : 484 pages
File Size : 53,9 Mb
Release : 2018-06-01
Category : Geometry, Algebraic
ISBN : 9781470435189

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Introduction to Algebraic Geometry by Steven Dale Cutkosky Pdf

This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.

Author : Serge Lang
Publisher : Courier Dover Publications
Page : 273 pages
File Size : 48,5 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9780486839806

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Introduction to Algebraic Geometry by Serge Lang Pdf

Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.

Author : Daniel Perrin
Publisher : Springer Science & Business Media
Page : 267 pages
File Size : 55,7 Mb
Release : 2007-12-16
Category : Mathematics
ISBN : 9781848000568

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Algebraic Geometry by Daniel Perrin Pdf

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.

Author : Igor Kriz,Sophie Kriz
Publisher : Springer Nature
Page : 481 pages
File Size : 55,8 Mb
Release : 2021-03-13
Category : Mathematics
ISBN : 9783030626440

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Introduction to Algebraic Geometry by Igor Kriz,Sophie Kriz Pdf

The goal of this book is to provide an introduction to algebraic geometry accessible to students. Starting from solutions of polynomial equations, modern tools of the subject soon appear, motivated by how they improve our understanding of geometrical concepts. In many places, analogies and differences with related mathematical areas are explained. The text approaches foundations of algebraic geometry in a complete and self-contained way, also covering the underlying algebra. The last two chapters include a comprehensive treatment of cohomology and discuss some of its applications in algebraic geometry.

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 49,9 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 : Justin R. Smith
Publisher : Justin Smith
Page : 637 pages
File Size : 48,7 Mb
Release : 2014
Category : Mathematics
ISBN : 9781503381537

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Introduction to Algebraic Geometry by Justin R. Smith Pdf

This book is intended for self-study or as a textbook for graduate students or advanced undergraduates. It presupposes some basic knowledge of point-set topology and a solid foundation in linear algebra. Otherwise, it develops all of the commutative algebra, sheaf-theory and cohomology needed to understand the material. It also presents applications to robotics and other fields.

Author : Ciro Ciliberto
Publisher : Springer Nature
Page : 327 pages
File Size : 46,7 Mb
Release : 2021-05-05
Category : Mathematics
ISBN : 9783030710217

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An Undergraduate Primer in Algebraic Geometry by Ciro Ciliberto Pdf

This book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems. The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology. This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.

Author : Meinolf Geck
Publisher : Oxford University Press
Page : 321 pages
File Size : 49,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9780199676163

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An Introduction to Algebraic Geometry and Algebraic Groups by Meinolf Geck Pdf

An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.

Author : Brendan Hassett
Publisher : Unknown
Page : 252 pages
File Size : 40,6 Mb
Release : 2007
Category : Geometry, Algebraic
ISBN : 0511573626

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Introduction to Algebraic Geometry by Brendan Hassett Pdf

Central concepts most useful for computation; for undergraduate/graduate students in mathematics, researchers in applications.

Author : Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 49,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475744972

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An Invitation to Algebraic Geometry by Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves Pdf

This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Author : Ernst Kunz
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 48,8 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 9781461459873

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Introduction to Commutative Algebra and Algebraic Geometry by Ernst Kunz Pdf

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.

Author : Joe Harris
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 41,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475721898

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Algebraic Geometry by Joe Harris Pdf

"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

Author : Kenji Ueno
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 40,5 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 : Alan David Thomas
Publisher : Pitman Publishing
Page : 256 pages
File Size : 45,8 Mb
Release : 1977
Category : Mathematics
ISBN : UOM:49015000693995

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Zeta-functions by Alan David Thomas Pdf

Author : Igor Rostislavovich Shafarevich
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 48,7 Mb
Release : 1994
Category : Mathematics
ISBN : 3540575545

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Basic Algebraic Geometry 2 by Igor Rostislavovich Shafarevich Pdf

The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with Volume 1 the author has revised the text and added new material, e.g. a section on real algebraic curves. Although the material is more advanced than in Volume 1 the algebraic apparatus is kept to a minimum making the book accessible to non-specialists. It can be read independently of Volume 1 and is suitable for beginning graduate students in mathematics as well as in theoretical physics.