Algebraic Geometry I Schemes

Author : Ulrich Görtz,Torsten Wedhorn
Publisher : Springer Nature
Page : 626 pages
File Size : 54,9 Mb
Release : 2020-07-27
Category : Mathematics
ISBN : 9783658307332

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Algebraic Geometry I: Schemes by Ulrich Görtz,Torsten Wedhorn Pdf

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.

Author : Ulrich Görtz,Torsten Wedhorn
Publisher : Springer Science & Business Media
Page : 615 pages
File Size : 51,5 Mb
Release : 2010-08-09
Category : Mathematics
ISBN : 9783834897220

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Algebraic Geometry by Ulrich Görtz,Torsten Wedhorn Pdf

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.

Author : David Eisenbud,Joe Harris
Publisher : Springer Science & Business Media
Page : 340 pages
File Size : 41,8 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387226392

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The Geometry of Schemes by David Eisenbud,Joe Harris Pdf

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.

Author : 健爾·上野,上野健爾
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 40,9 Mb
Release : 1999
Category : Geometry, Algebraic
ISBN : 9780821808627

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Algebraic Geometry 1 by 健爾·上野,上野健爾 Pdf

By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.

Author : V.I. Danilov,V.V. Shokurov
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 49,8 Mb
Release : 1998-03-17
Category : Mathematics
ISBN : 3540637052

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Algebraic Geometry I by V.I. Danilov,V.V. Shokurov Pdf

"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum

Author : Igor Rostislavovich Shafarevich
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 49,5 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.

Author : David Mumford
Publisher : Springer
Page : 314 pages
File Size : 49,7 Mb
Release : 2004-02-24
Category : Mathematics
ISBN : 9783540460213

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The Red Book of Varieties and Schemes by David Mumford Pdf

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.

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 42,8 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 : Audun Holme
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 42,6 Mb
Release : 2011-10-06
Category : Mathematics
ISBN : 3642192254

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A Royal Road to Algebraic Geometry by Audun Holme Pdf

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!

Author : Siegfried Bosch
Publisher : Springer Nature
Page : 504 pages
File Size : 54,9 Mb
Release : 2022-04-22
Category : Mathematics
ISBN : 9781447175230

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Algebraic Geometry and Commutative Algebra by Siegfried Bosch Pdf

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. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s by inventing schemes. Schemes now also play an important role in Algebraic Number Theory, a field that used to be far away from Geometry. The new point of view paved the way for spectacular progress, such as the proof of Fermat's Last Theorem by Wiles and Taylor. This book explains the scheme-theoretic approach to Algebraic Geometry for non-experts, while more advanced readers can use it to broaden their view on the subject. A separate part presents the necessary prerequisites from Commutative Algebra, thereby providing an accessible and self-contained introduction to advanced Algebraic Geometry. Every chapter of the book is preceded by a motivating introduction with an informal discussion of its contents and background. Typical examples, and an abundance of exercises illustrate each section. Therefore the book is an excellent companion for self-studying or for complementing skills that have already been acquired. It can just as well serve as a convenient source for (reading) course material and, in any case, as supplementary literature. The present edition is a critical revision of the earlier text.

Author : Qing Liu,Reinie Erne
Publisher : Oxford University Press
Page : 593 pages
File Size : 45,6 Mb
Release : 2006-06-29
Category : Mathematics
ISBN : 9780191547805

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Algebraic Geometry and Arithmetic Curves by Qing Liu,Reinie Erne Pdf

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.

Author : André 1906- Weil
Publisher : Hassell Street Press
Page : 392 pages
File Size : 54,5 Mb
Release : 2021-09-10
Category : Electronic
ISBN : 1015107672

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Foundations of Algebraic Geometry. --; 29 by André 1906- Weil Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Edoardo Sernesi
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 54,7 Mb
Release : 2007-04-20
Category : Mathematics
ISBN : 9783540306153

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Deformations of Algebraic Schemes by Edoardo Sernesi Pdf

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.

Author : Daniel Perrin
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 55,9 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 : Ian Grant Macdonald
Publisher : Unknown
Page : 136 pages
File Size : 42,5 Mb
Release : 1968
Category : Algebraic topology
ISBN : STANFORD:36105031253599

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Algebraic Geometry by Ian Grant Macdonald Pdf