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| Author | : Ulrich Görtz |
| Publisher | : Springer Nature |
| Total Pages | : 626 |
| Release | : 2020-07-27 |
| Genre | : Mathematics |
| ISBN | : 3658307331 |
Download Algebraic Geometry I: Schemes Book in PDF, ePub and Kindle
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 |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 615 |
| Release | : 2010-08-09 |
| Genre | : Mathematics |
| ISBN | : 3834897221 |
Download Algebraic Geometry Book in PDF, ePub and Kindle
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 | : Steven Dale Cutkosky |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 484 |
| Release | : 2018-06-01 |
| Genre | : Geometry, Algebraic |
| ISBN | : 1470435187 |
Download Introduction to Algebraic Geometry Book in PDF, ePub and Kindle
This book presents a readable and accessible introductory course in algebraic geometry, with most of the fundamental classical results presented with complete proofs. An emphasis is placed on developing connections between geometric and algebraic aspects of the theory. Differences between the theory in characteristic and positive characteristic are emphasized. The basic tools of classical and modern algebraic geometry are introduced, including varieties, schemes, singularities, sheaves, sheaf cohomology, and intersection theory. Basic classical results on curves and surfaces are proved. More advanced topics such as ramification theory, Zariski's main theorem, and Bertini's theorems for general linear systems are presented, with proofs, in the final chapters. With more than 200 exercises, the book is an excellent resource for teaching and learning introductory algebraic geometry.
| Author | : V.I. Danilov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 328 |
| Release | : 1998-03-17 |
| Genre | : Mathematics |
| ISBN | : 9783540637059 |
Download Algebraic Geometry I Book in PDF, ePub and Kindle
"... 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 | : 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 | : Igor Rostislavovich Shafarevich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 292 |
| Release | : 1994 |
| Genre | : Mathematics |
| ISBN | : 9783540575542 |
Download Basic Algebraic Geometry 2 Book in PDF, ePub and Kindle
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 | : R.K. Lazarsfeld |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 414 |
| Release | : 2004-08-24 |
| Genre | : History |
| ISBN | : 9783540225331 |
Download Positivity in Algebraic Geometry I Book in PDF, ePub and Kindle
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.
| Author | : David Mumford |
| Publisher | : Springer |
| Total Pages | : 208 |
| Release | : 1976 |
| Genre | : Mathematics |
| ISBN | : |
Download Algebraic Geometry I Book in PDF, ePub and Kindle
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
| Author | : Günter Harder |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 301 |
| Release | : 2008-08-01 |
| Genre | : Mathematics |
| ISBN | : 3834895016 |
Download Lectures on Algebraic Geometry I Book in PDF, ePub and Kindle
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own. In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
| Author | : Serge Lang |
| Publisher | : Courier Dover Publications |
| Total Pages | : 273 |
| Release | : 2019-03-20 |
| Genre | : Mathematics |
| ISBN | : 048683980X |
Download Introduction to Algebraic Geometry Book in PDF, ePub and Kindle
Author Serge Lang defines algebraic geometry as the study of systems of algebraic equations in several variables and of the structure that one can give to the solutions of such equations. The study can be carried out in four ways: analytical, topological, algebraico-geometric, and arithmetic. This volume offers a rapid, concise, and self-contained introductory approach to the algebraic aspects of the third method, the algebraico-geometric. The treatment assumes only familiarity with elementary algebra up to the level of Galois theory. Starting with an opening chapter on the general theory of places, the author advances to examinations of algebraic varieties, the absolute theory of varieties, and products, projections, and correspondences. Subsequent chapters explore normal varieties, divisors and linear systems, differential forms, the theory of simple points, and algebraic groups, concluding with a focus on the Riemann-Roch theorem. All the theorems of a general nature related to the foundations of the theory of algebraic groups are featured.
