Basic Algebraic Geometry 1Basic Algebraic Geometry 1



'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles.

Author: Igor R. Shafarevich

Publisher: Springer Science & Business Media

ISBN: 9783642379567

Category:

Page: 310

View: 769

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.

Basic Algebraic Geometry 1Basic Algebraic Geometry 1



This book is a revised and expanded new edition of the first four chapters of Shafarevich’s well-known introductory book on algebraic geometry.

Author: Igor R. Shafarevich

Publisher: Springer Science & Business Media

ISBN: 9783642579080

Category:

Page: 304

View: 544

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.

Basic Algebraic Geometry 2Basic Algebraic Geometry 2



The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with first volume the author has revised the text and added new material.

Author: Igor R. Shafarevich

Publisher: Springer

ISBN: 9783642579561

Category:

Page: 270

View: 333

The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with first volume the author has revised the text and added new material. 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 the first volume and is suitable for beginning graduate students.

Basic Algebraic GeometryBasic Algebraic Geometry



Author: Igorʹ Rostislavovich Shafarevich

Publisher: Springer

ISBN: 0387066918

Category:

Page: 439

View: 691

The second volume of Shafarevich's introductory book on algebraic varieties and complex manifolds. As with Volume 1, the author has revised the text and added new material, e.g. as 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 those in theoretical physics.

Algebraic Geometry 1Algebraic Geometry 1



Beginning algebraic geometers are well served by Uneno's inviting introduction to the language of schemes.

Author: 健爾·上野

Publisher: American Mathematical Soc.

ISBN: 0821808621

Category:

Page: 154

View: 463

Beginning algebraic geometers are well served by Uneno's inviting introduction to the language of schemes. Grothendieck's schemes and Zariski's emphasis on algebra and rigor are primary sources for this introduction to a rich mathematical subject. Ueno's book is a self-contained text suitable for an introductory course on algebraic geometry.

Algebraic Geometry IAlgebraic Geometry I



From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most ...

Author: David Mumford

Publisher: Springer Science & Business Media

ISBN: 3540586571

Category:

Page: 186

View: 604

From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!" Zentralblatt

Algebraic GeometryAlgebraic Geometry



"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way.

Author: Joe Harris

Publisher: Springer Science & Business Media

ISBN: 9780387977164

Category:

Page: 328

View: 440

"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

Algebraic GeometryAlgebraic Geometry



This book introduces the reader to modern algebraic geometry.

Author: Ulrich Görtz

Publisher: Springer Science & Business Media

ISBN: 9783834897220

Category:

Page: 615

View: 466

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.

Algebraic Geometry and Commutative AlgebraAlgebraic Geometry and Commutative Algebra



The book provides an accessible and self-contained introduction to algebraic geometry, up to an advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents.

Author: Siegfried Bosch

Publisher: Springer Science & Business Media

ISBN: 9781447148296

Category:

Page: 504

View: 444

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.

Algebraic GeometryAlgebraic Geometry



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 ...

Author: Daniel Perrin

Publisher: Springer Science & Business Media

ISBN: 1848000561

Category:

Page: 263

View: 585

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.

Hodge Theory and Complex Algebraic Geometry I Volume 1Hodge Theory and Complex Algebraic Geometry I Volume 1



The text is complemented by exercises which provide useful results in complex algebraic geometry.

Author: Claire Voisin

Publisher: Cambridge University Press

ISBN: 1139437690

Category:

Page:

View: 464

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

Computer Graphics and Geometric Modeling MathematicsComputer Graphics and Geometric Modeling Mathematics



[ Hoff93 ] Hoffmann , Christoph M . , “ Implicit Curves and Surfaces in CAGD , ”
CG & A , 13 ( 1 ) , January 1993 , 79 – 88 . ... ( Shaf94 ] Shafarevich , Igor R . ,
Basic Algebraic Geometry 1 , 2nd Edition , Springer - Verlag , 1994 . [ Walk50 ]
Walker ...

Author: Max K Agoston

Publisher:

ISBN: UCSD:31822033230939

Category:

Page:

View: 701

Positivity in Algebraic Geometry IPositivity in Algebraic Geometry I



This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity.

Author: R.K. Lazarsfeld

Publisher: Springer Science & Business Media

ISBN: 3540225331

Category:

Page: 387

View: 997

This two volume work on Positivity in Algebraic Geometry contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Volume I is more elementary than Volume II, and, for the most part, it can be read without access to Volume II.

Algebraic GeometryAlgebraic Geometry



In this chapter we develop the basic theory of schemes, following Grothendieck [
EGA]. Sections 1 to 5 are fundamental. They contain a review of sheaf theory (
necessary even to define a scheme), then the basic definitions of schemes, ...

Author: Robin Hartshorne

Publisher: Springer Science & Business Media

ISBN: 9781475738490

Category:

Page: 496

View: 659

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.

Elementary Algebraic GeometryElementary Algebraic Geometry



D. Mumford, Algebraic Geometry I: Complea Projective Varieties. Springer-Verlag
1996. M. Reid, Undergraduate Algebraic Geometry. LMS Student Texts 12,
Cambridge University Press 1988. I. R. Shafarevich, Basic Algebraic Geometry 1,
2, ...

Author: Klaus Hulek

Publisher: American Mathematical Soc.

ISBN: 9780821829523

Category:

Page: 213

View: 995

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.

Commutative AlgebraCommutative Algebra



This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with ...

Author: David Eisenbud

Publisher: Springer Science & Business Media

ISBN: 9781461253501

Category:

Page: 800

View: 327

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.