introduction-to-algebraic-geometry

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Introduction To Algebraic Geometry

Author : Justin R. Smith
ISBN : 9781503381537
Genre : Geometry, Algebraic
File Size : 78. 86 MB
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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.

An Introduction To Algebraic Geometry

Author : Kenji Ueno
ISBN : 9780821811443
Genre : Mathematics
File Size : 69. 13 MB
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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.

Introduction To Algebraic Geometry

Author : John Greenlees Semple
ISBN : UOM:49015000693938
Genre : Geometry, Algebraic.
File Size : 65. 95 MB
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This classic work, now available in paperback, outlines the geometric aspects of algebraic equations, one of the oldest and most central subjects in mathematics. Recent decades have seen explosive growth in the more abstract side of algeraic geometry, with great emphasis on new basic techniques. This timely reissue complements these recent innovations, providing a much-needed background in such areas as plane curves, quadratic transformations, the geometry of line systems, and the projective characters of curves and surfaces. Providing a wealth of definitive material, this work will appeal to those interested in algebraic geometry and in more modern abstract studies.

An Introduction To Algebraic Geometry And Algebraic Groups

Author : Meinolf Geck
ISBN : 9780191663727
Genre : Mathematics
File Size : 70. 32 MB
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An accessible text introducing algebraic geometries and algebraic groups at advanced undergraduate and early graduate level, this book develops the language of algebraic geometry from scratch and uses it to set up the theory of affine algebraic groups from first principles. Building on the background material from algebraic geometry and algebraic groups, the text provides an introduction to more advanced and specialised material. An example is the representation theory of finite groups of Lie type. The text covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, a thorough treatment of Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields. Experts in the field will enjoy some of the new approaches to classical results. The text uses algebraic groups as the main examples, including worked out examples, instructive exercises, as well as bibliographical and historical remarks.

Introduction To Algebraic Geometry

Author : Serge Lang
ISBN : 9780486834221
Genre : Mathematics
File Size : 88. 7 MB
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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.

Algebraic Geometry

Author : S. Iitaka
ISBN : UOM:49015000693433
Genre : Mathematics
File Size : 59. 31 MB
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The aim of this book is to introduce the reader to the geometric theory of algebraic varieties, in particular to the birational geometry of algebraic varieties. This volume grew out of the author's book in Japanese published in 3 volumes by Iwanami, Tokyo, in 1977. While writing this English version, the author has tried to rearrange and rewrite the original material so that even beginners can read it easily without referring to other books, such as textbooks on commutative algebra. The reader is only expected to know the definition of Noetherin rings and the statement of the Hilbert basis theorem. The new chapters 1, 2, and 10 have been expanded. In particular, the exposition of D-dimension theory, although shorter, is more complete than in the old version. However, to keep the book of manageable size, the latter parts of Chapters 6, 9, and 11 have been removed. I thank Mr. A. Sevenster for encouraging me to write this new version, and Professors K. K. Kubota in Kentucky and P. M. H. Wilson in Cam bridge for their careful and critical reading of the English manuscripts and typescripts. I held seminars based on the material in this book at The University of Tokyo, where a large number of valuable comments and suggestions were given by students Iwamiya, Kawamata, Norimatsu, Tobita, Tsushima, Maeda, Sakamoto, Tsunoda, Chou, Fujiwara, Suzuki, and Matsuda.

Elementary Algebraic Geometry

Author : Klaus Hulek
ISBN : 9780821829523
Genre : Mathematics
File Size : 83. 23 MB
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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.

Introduction To Algebraic Geometry And Commutative Algebra

Author : Dilip P. Patil
ISBN : 9789814304573
Genre : Mathematics
File Size : 83. 47 MB
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Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. With concise yet clear definitions and synopses a selection is made from the wealth of meterial in the disciplines including the Riemann-Roch theorem for arbitrary projective curves."--pub. desc.

Algebraic Geometry And Commutative Algebra

Author : Siegfried Bosch
ISBN : 9781447148296
Genre : Mathematics
File Size : 27. 8 MB
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Algebraic geometry is a fascinating branch of mathematics that combines methods from both, algebra and geometry. It transcends the limited scope of pure algebra by means of geometric construction principles. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.

Introduction To Algebraic Geometry

Author : David Mumford
ISBN : OCLC:1024699932
Genre :
File Size : 45. 65 MB
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Introduction To Algebraic Geometry

Author : Brendan Hassett
ISBN : 9781139464598
Genre : Mathematics
File Size : 58. 93 MB
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Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

Introduction To Commutative Algebra And Algebraic Geometry

Author : Ernst Kunz
ISBN : 9781461459873
Genre : Mathematics
File Size : 83. 91 MB
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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.

Introduction To Algebraic Geometry And Algebraic Groups

Author :
ISBN : 008087150X
Genre : Mathematics
File Size : 62. 42 MB
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Introduction to Algebraic Geometry and Algebraic Groups

Introduction To Algebraic Geometry

Author : Justin Smith
ISBN : 1466572485
Genre : Mathematics
File Size : 28. 18 MB
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Unlike other books on algebraic geometry, this text includes applications from various areas of mathematics, biology, and physics. Designed for advanced undergraduate and graduate students with an applied mathematics background, the book develops most of the necessary commutative algebra. It describes all of the algebraic and geometric concepts required for understanding algebraic geometry. The author also presents a very recent and simpler proof of the dimension of an affine variety. A solutions manual and figure slides are available with qualifying course adoption.

Introduction To Algebraic Geometry Through Affine Algebraic Groups

Author : Alain Robert
ISBN : STANFORD:36105031715449
Genre : Affine algebraic groups
File Size : 20. 24 MB
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Algebraic Curves

Author : William Fulton
ISBN : UOM:39015050421349
Genre : Mathematics
File Size : 33. 10 MB
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Introduction To Algebraic Geometry

Author : W. Gordon Welchman
ISBN : 9781316601808
Genre : Mathematics
File Size : 70. 83 MB
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Originally published in 1950, this textbook studies projective geometry and provides a solid introduction to similar studies in space of more than two dimensions.

Basic Algebraic Geometry 1

Author : Igor R. Shafarevich
ISBN : 9783642579080
Genre : Mathematics
File Size : 79. 50 MB
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This book is a revised and expanded new edition of the first four chapters of Shafarevich’s well-known introductory book on algebraic geometry. Besides correcting misprints and inaccuracies, the author has added plenty of new material, mostly concrete geometrical material such as Grassmannian varieties, plane cubic curves, the cubic surface, degenerations of quadrics and elliptic curves, the Bertini theorems, and normal surface singularities.

Ideals Varieties And Algorithms

Author : David Cox
ISBN : 9781475726930
Genre : Mathematics
File Size : 78. 68 MB
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Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. The book bases its discussion of algorithms on a generalisation of the division algorithm for polynomials in one variable that was only discovered in the 1960's. Although the algorithmic roots of algebraic geometry are old, the computational aspects were neglected earlier in this century. This has changed in recent years, and new algorithms, coupled with the power of fast computers, have let to some interesting applications, for example in robotics and in geometric theorem proving. In preparing this new edition, the authors present an improved proof of the Buchberger Criterion as well as a proof of Bezout's Theorem.

Introduction To Algebraic Geometry

Author : John G. Semple
ISBN : OCLC:1072984454
Genre :
File Size : 22. 55 MB
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