Undergraduate Algebraic Geometry

Undergraduate Algebraic Geometry PDF Book Detail:
Author: Miles Reid
Publisher: Cambridge University Press
ISBN: 9780521356626
Size: 72.36 MB
Format: PDF, Docs
Category : Mathematics
Languages : en
Pages : 129
View: 6605

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Book Description: This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.

Algebraic Geometry And Commutative Algebra

Algebraic Geometry and Commutative Algebra PDF Book Detail:
Author: Siegfried Bosch
Publisher: Springer Science & Business Media
ISBN: 1447148290
Size: 79.47 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 504
View: 4435

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Book Description: 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.

Elementary Algebraic Geometry

Elementary Algebraic Geometry PDF Book Detail:
Author: Klaus Hulek
Publisher: American Mathematical Soc.
ISBN: 0821829521
Size: 26.50 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 213
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Book Description: 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.

Algebraic Geometry

Algebraic Geometry PDF Book Detail:
Author: Robin Hartshorne
Publisher: Springer Science & Business Media
ISBN: 1475738498
Size: 38.90 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 496
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Book Description: 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.

Algebraic Geometry Ii

Algebraic Geometry II PDF Book Detail:
Author: I.R. Shafarevich
Publisher: Springer Science & Business Media
ISBN: 3642609252
Size: 70.78 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 264
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Book Description: This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

An Invitation To Algebraic Geometry

An Invitation to Algebraic Geometry PDF Book Detail:
Author: Karen Smith
Publisher: Springer Science & Business Media
ISBN: 9780387989808
Size: 35.78 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 164
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Book Description: This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Basic Algebraic Geometry 2

Basic Algebraic Geometry 2 PDF Book Detail:
Author: Igor R. Shafarevich
Publisher: Springer Science & Business Media
ISBN: 3642380107
Size: 23.90 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 262
View: 1943

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Book Description: 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 second volume is in two parts: Book II is a gentle cultural introduction to scheme theory, with the first aim of putting abstract algebraic varieties on a firm foundation; a second aim is to introduce Hilbert schemes and moduli spaces, that serve as parameter spaces for other geometric constructions. Book III discusses complex manifolds and their relation with algebraic varieties, Kähler geometry and Hodge theory. The final section raises an important problem in uniformising higher dimensional varieties that has been widely studied as the ``Shafarevich conjecture''. The style of Basic Algebraic Geometry 2 and its minimal prerequisites make it to a large extent independent of Basic Algebraic Geometry 1, and accessible to beginning graduate students in mathematics and in theoretical physics.

History Algebraic Geometry

History Algebraic Geometry PDF Book Detail:
Author: Suzanne C. Dieudonne
Publisher: Routledge
ISBN: 1351440535
Size: 32.69 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 186
View: 6852

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Book Description: This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.

Computational Algebraic Geometry

Computational Algebraic Geometry PDF Book Detail:
Author: HENRY SCHENCK
Publisher: Cambridge University Press
ISBN: 9780521536509
Size: 65.40 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 193
View: 6211

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Book Description: Table of contents

Algebraic Geometry

Algebraic Geometry PDF Book Detail:
Author: Ulrich Görtz
Publisher: Springer Science & Business Media
ISBN: 3834897221
Size: 75.92 MB
Format: PDF, ePub
Category : Mathematics
Languages : en
Pages : 615
View: 1657

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Book Description: 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.