Principles Of Algebraic Geometry PDF Download
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Author | : Phillip Griffiths |
Publisher | : John Wiley & Sons |
Total Pages | : 837 |
Release | : 2014-08-21 |
Genre | : Mathematics |
ISBN | : 111862632X |
Download Principles of Algebraic Geometry Book in PDF, ePub and Kindle
A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.
Author | : Daniel Huybrechts |
Publisher | : Springer Science & Business Media |
Total Pages | : 336 |
Release | : 2005 |
Genre | : Computers |
ISBN | : 9783540212904 |
Download Complex Geometry Book in PDF, ePub and Kindle
Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)
Author | : Qing Liu |
Publisher | : Oxford University Press |
Total Pages | : 593 |
Release | : 2006-06-29 |
Genre | : Mathematics |
ISBN | : 0191547808 |
Download Algebraic Geometry and Arithmetic Curves Book in PDF, ePub and Kindle
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 | : Karen E. Smith |
Publisher | : Springer Science & Business Media |
Total Pages | : 173 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 1475744978 |
Download An Invitation to Algebraic Geometry Book in PDF, ePub and Kindle
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.
Author | : Siegfried Bosch |
Publisher | : Springer Nature |
Total Pages | : 504 |
Release | : 2022-04-22 |
Genre | : Mathematics |
ISBN | : 1447175239 |
Download Algebraic Geometry and Commutative Algebra Book in PDF, ePub and Kindle
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 | : Robin Hartshorne |
Publisher | : Springer Science & Business Media |
Total Pages | : 511 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1475738498 |
Download Algebraic Geometry Book in PDF, ePub and Kindle
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 | : Rick Miranda |
Publisher | : American Mathematical Soc. |
Total Pages | : 414 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : 0821802682 |
Download Algebraic Curves and Riemann Surfaces Book in PDF, ePub and Kindle
In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book begins as a primer on Riemann surfaces, with complex charts and meromorphic functions taking centre stage. But the main examples come fromprojective curves, and slowly but surely the text moves toward the algebraic category. Proofs of the Riemann-Roch and Serre Dualtiy Theorems are presented in an algebraic manner, via an adaptation of the adelic proof, expressed completely in terms of solving a Mittag-Leffler problem. Sheaves andcohomology are introduced as a unifying device in the later chapters, so that their utility and naturalness are immediately obvious. Requiring a background of one term of complex variable theory and a year of abstract algebra, this is an excellent graduate textbook for a second-term course in complex variables or a year-long course in algebraic geometry.
Author | : Joe Harris |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2013-11-11 |
Genre | : Mathematics |
ISBN | : 1475721897 |
Download Algebraic Geometry Book in PDF, ePub and Kindle
"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
Author | : Henry Frederick Baker |
Publisher | : |
Total Pages | : 204 |
Release | : 1922 |
Genre | : Geometry |
ISBN | : |
Download Principles of Geometry Book in PDF, ePub and Kindle
Author | : Meinolf Geck |
Publisher | : Oxford University Press |
Total Pages | : 321 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 019967616X |
Download An Introduction to Algebraic Geometry and Algebraic Groups Book in PDF, ePub and Kindle
An accessible text introducing algebraic groups at advanced undergraduate and early graduate level, this book covers the conjugacy of Borel subgroups and maximal tori, the theory of algebraic groups with a BN-pair, Frobenius maps on affine varieties and algebraic groups, zeta functions and Lefschetz numbers for varieties over finite fields.