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Title The Red Book of Varieties and Schemes
Author David Mumford
Publisher Springer
Release Date 2004-02-24
Category Mathematics
Total Pages 314
ISBN 9783540460213
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 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 Curves and their Jacobians
Author David Mumford
Publisher Unknown
Release Date 1978
Category
Total Pages 104
ISBN OCLC:630214524
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:

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 Ian Grant Macdonald

Title Algebraic Geometry
Author Ian Grant Macdonald
Publisher Unknown
Release Date 1968
Category Algebraic topology
Total Pages 113
ISBN STANFORD:36105031253599
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.

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 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 Lectures on Curves on an Algebraic Surface
Author David Mumford
Publisher Princeton University Press
Release Date 1966-08-21
Category Mathematics
Total Pages 200
ISBN 0691079935
Language English, Spanish, and French
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Book Summary:

These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.

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.

Title Foundations of Algebraic Geometry
Author André Weil
Publisher American Mathematical Soc.
Release Date 1947
Category Geometry, Algebraic
Total Pages 288
ISBN UCBK:C065392060
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 2013-03-09
Category Mathematics
Total Pages 372
ISBN 9783662124925
Language English, Spanish, and French
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Book Summary:

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. It describes relations with standard cohomology theory and provides complete proofs. Coverage also presents basic concepts and results of homotopical algebra. This second edition contains numerous corrections.

3264 And All That by David Eisenbud

Title 3264 and All That
Author David Eisenbud
Publisher Cambridge University Press
Release Date 2016-04-14
Category Mathematics
Total Pages 616
ISBN 9781107017085
Language English, Spanish, and French
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Book Summary:

3264, the mathematical solution to a question concerning geometric figures.

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.

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:

Title Deformations of Algebraic Schemes
Author Edoardo Sernesi
Publisher Springer Science & Business Media
Release Date 2007-04-20
Category Mathematics
Total Pages 342
ISBN 9783540306153
Language English, Spanish, and French
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Book Summary:

This account of deformation theory in classical algebraic geometry over an algebraically closed field presents for the first time some results previously scattered in the literature, with proofs that are relatively little known, yet relevant to algebraic geometers. Many examples are provided. Most of the algebraic results needed are proved. The style of exposition is kept at a level amenable to graduate students with an average background in algebraic geometry.

Abelian Varieties by David Mumford

Title Abelian Varieties
Author David Mumford
Publisher Amer Mathematical Society
Release Date 2008-01-01
Category Mathematics
Total Pages 263
ISBN 8185931860
Language English, Spanish, and French
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Book Summary:

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 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.