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Title The Red Book of Varieties and Schemes
Author David Mumford
Publisher Springer
Release Date 2013-11-11
Category Mathematics
Total Pages 315
ISBN 9783662215814
Language English, Spanish, and French
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Book Summary:

"The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. Springer-Verlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)

Title The Red Book of Varieties and Schemes
Author David Mumford
Publisher Unknown
Release Date 1995
Category
Total Pages 308
ISBN OCLC:245822010
Language English, Spanish, and French
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Book Summary:

Title Algebraic geometry
Author Anonim
Publisher Unknown
Release Date 2021
Category
Total Pages 86
ISBN OCLC:643072049
Language English, Spanish, and French
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Book Summary:

The Geometry Of Schemes by David Eisenbud

Title The Geometry of Schemes
Author David Eisenbud
Publisher Springer Science & Business Media
Release Date 2006-04-06
Category Mathematics
Total Pages 300
ISBN 9780387226392
Language English, Spanish, and French
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Book Summary:

Grothendieck’s beautiful theory of schemes permeates modern algebraic geometry and underlies its applications to number theory, physics, and applied mathematics. This simple account of that theory emphasizes and explains the universal geometric concepts behind the definitions. In the book, concepts are illustrated with fundamental examples, and explicit calculations show how the constructions of scheme theory are carried out in practice.

Title Algebraic Geometry and Commutative Algebra
Author Siegfried Bosch
Publisher Springer Science & Business Media
Release Date 2012-11-15
Category Mathematics
Total Pages 504
ISBN 9781447148296
Language English, Spanish, and French
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Book Summary:

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.

Title Groups Trees and Projective Modules
Author W. Dicks
Publisher Springer
Release Date 2006-11-15
Category Mathematics
Total Pages 132
ISBN 9783540392101
Language English, Spanish, and French
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Book Summary:

Algebraic Geometry by Daniel Perrin

Title Algebraic Geometry
Author Daniel Perrin
Publisher Springer Science & Business Media
Release Date 2007-12-16
Category Mathematics
Total Pages 263
ISBN 1848000561
Language English, Spanish, and French
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Book Summary:

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.

Algebraic Geometry I by David Mumford

Title Algebraic Geometry I
Author David Mumford
Publisher Springer
Release Date 1976
Category Algebraic varieties
Total Pages 186
ISBN UOM:39015015620209
Language English, Spanish, and French
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Book Summary:

Methods Of Homological Algebra by Sergei I. Gelfand

Title Methods of Homological Algebra
Author Sergei I. Gelfand
Publisher Springer Science & Business Media
Release Date 2013-04-17
Category Mathematics
Total Pages 374
ISBN 9783662032206
Language English, Spanish, and French
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Book Summary:

Homological algebra first arose as a language for describing topological prospects of geometrical objects. As with every successful language it quickly expanded its coverage and semantics, and its contemporary applications are many and diverse. This modern approach to homological algebra, by two leading writers in the field, is based on the systematic use of the language and ideas of derived categories and derived functors. Relations with standard cohomology theory (sheaf cohomology, spectral sequences, etc.) are described. In most cases complete proofs are given. Basic concepts and results of homotopical algebra are also presented. The book addresses people who want to learn about a modern approach to homological algebra and to use it in their work.

Algebraic Geometry by Ulrich Görtz

Title Algebraic Geometry
Author Ulrich Görtz
Publisher Springer Science & Business Media
Release Date 2010-08-09
Category Mathematics
Total Pages 615
ISBN 9783834897220
Language English, Spanish, and French
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Book Summary:

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.

Title Rational Curves on Algebraic Varieties
Author Janos Kollar
Publisher Springer Science & Business Media
Release Date 1999-06-22
Category Mathematics
Total Pages 321
ISBN 3540601686
Language English, Spanish, and French
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Book Summary:

The aim of this book is to provide an introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especially rational curves, on varieties. The main applications are in the study of Fano varieties and of related varieties with lots of rational curves on them. This Ergebnisse volume provides the first systematic introduction to this field of study. The book contains a large number of examples and exercises which serve to illustrate the range of the methods and also lead to many open questions of current research.

Algebraic Geometry by Robin Hartshorne

Title Algebraic Geometry
Author Robin Hartshorne
Publisher Springer Science & Business Media
Release Date 2013-06-29
Category Mathematics
Total Pages 496
ISBN 9781475738490
Language English, Spanish, and French
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Book Summary:

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.

Title Quotations from Chairman Mao Tse tung
Author Zedong Mao
Publisher Unknown
Release Date 1967
Category China
Total Pages 179
ISBN UCSD:31822012835799
Language English, Spanish, and French
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Book Summary:

Reveals the man and the aims of the Cultural Revolution.

Title Conformal Field Theory with Gauge Symmetry
Author Kenji Ueno
Publisher American Mathematical Soc.
Release Date 2008
Category Mathematics
Total Pages 168
ISBN 9780821840887
Language English, Spanish, and French
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Book Summary:

This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces with coordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection--one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over $\mathbb{P}^1$. Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.

Title Algebraic Geometry and Arithmetic Curves
Author Qing Liu
Publisher Oxford University Press
Release Date 2006-06-29
Category Mathematics
Total Pages 592
ISBN 9780191547805
Language English, Spanish, and French
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Book Summary:

This book is a general introduction to the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, regularity, Zariski's Main Theorem). This is followed by the more global aspect: coherent sheaves and a finiteness theorem for their cohomology groups. Then follows a chapter on sheaves of differentials, dualizing sheaves, and Grothendieck's duality theory. The first part ends with the theorem of Riemann-Roch and its application to the study of smooth projective curves over a field. Singular curves are treated through a detailed study of the Picard group. The second part starts with blowing-ups and desingularisation (embedded or not) of fibered surfaces over a Dedekind ring that leads on to intersection theory on arithmetic surfaces. Castelnuovo's criterion is proved and also the existence of the minimal regular model. This leads to the study of reduction of algebraic curves. The case of elliptic curves is studied in detail. The book concludes with the funadmental theorem of stable reduction of Deligne-Mumford. The book is essentially self-contained, including the necessary material on commutative algebra. The prerequisites are therefore few, and the book should suit a graduate student. It contains many examples and nearly 600 exercises.

Title Algebraic Varieties
Author G. Kempf
Publisher Cambridge University Press
Release Date 1993-09-09
Category Mathematics
Total Pages 163
ISBN 0521426138
Language English, Spanish, and French
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Book Summary:

An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.

Title The Red Book of Varieties and Schemes
Author David Mumford
Publisher Springer
Release Date 2014-03-12
Category Mathematics
Total Pages 314
ISBN 3662167670
Language English, Spanish, and French
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Book Summary:

Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.

Title A Royal Road to Algebraic Geometry
Author Audun Holme
Publisher Springer Science & Business Media
Release Date 2011-10-06
Category Mathematics
Total Pages 366
ISBN 3642192254
Language English, Spanish, and French
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Book Summary:

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!

Title Commutative Algebra Volume I
Author Oscar Zariski
Publisher Courier Dover Publications
Release Date 2019-11-13
Category Mathematics
Total Pages 352
ISBN 9780486836614
Language English, Spanish, and French
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Book Summary:

A precise, fundamental study of commutative algebra, this largely self-contained treatment is the first in a two-volume set. Intended for advanced undergraduates and graduate students in mathematics, its prerequisites are the rudiments of set theory and linear algebra, including matrices and determinants. The opening chapter develops introductory notions concerning groups, rings, fields, polynomial rings, and vector spaces. Subsequent chapters feature an exposition of field theory and classical material concerning ideals and modules in arbitrary commutative rings, including detailed studies of direct sum decompositions. The final two chapters explore Noetherian rings and Dedekind domains. This work prepares readers for the more advanced topics of Volume II, which include valuation theory, polynomial and power series rings, and local algebra.

Title Algebraic Geometry I Schemes
Author Ulrich Görtz
Publisher Springer Nature
Release Date 2020-07-27
Category Mathematics
Total Pages 626
ISBN 9783658307332
Language English, Spanish, and French
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Book Summary:

This book introduces the reader to modern algebraic geometry. It presents Grothendieck's technically demanding language of schemes that is the basis of the most important developments in the last fifty years within this area. A systematic treatment and motivation of the theory is emphasized, using concrete examples to illustrate its usefulness. Several examples from the realm of Hilbert modular surfaces and of determinantal varieties are used methodically to discuss the covered techniques. Thus the reader experiences that the further development of the theory yields an ever better understanding of these fascinating objects. The text is complemented by many exercises that serve to check the comprehension of the text, treat further examples, or give an outlook on further results. The volume at hand is an introduction to schemes. To get startet, it requires only basic knowledge in abstract algebra and topology. Essential facts from commutative algebra are assembled in an appendix. It will be complemented by a second volume on the cohomology of schemes.