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Author: Ulrich Görtz Publisher: Springer Science & Business Media ISBN: 3834897221 Category : Mathematics Languages : en Pages : 615
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.
Author: Ulrich Görtz Publisher: Springer Science & Business Media ISBN: 3834897221 Category : Mathematics Languages : en Pages : 615
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.
Author: Ulrich Görtz Publisher: Springer Nature ISBN: 3658307331 Category : Mathematics Languages : en Pages : 626
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.
Author: Steven Dale Cutkosky Publisher: American Mathematical Soc. ISBN: 1470435187 Category : Geometry, Algebraic Languages : en Pages : 484
Book Description
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: Robin Hartshorne Publisher: Springer Science & Business Media ISBN: 1475738498 Category : Mathematics Languages : en Pages : 511
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.
Author: V.I. Danilov Publisher: Springer Science & Business Media ISBN: 9783540637059 Category : Mathematics Languages : en Pages : 328
Book Description
"... 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: R.K. Lazarsfeld Publisher: Springer Science & Business Media ISBN: 9783540225331 Category : History Languages : en Pages : 414
Book Description
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: Igor Rostislavovich Shafarevich Publisher: Springer Science & Business Media ISBN: 9783540575542 Category : Mathematics Languages : en Pages : 292
Book Description
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: Solomon Lefschetz Publisher: ISBN: 9780691653242 Category : Languages : en Pages : 0
Book Description
The first application of modern algebraic techniques to a comprehensive selection of classical geometric problems. Written with spirit and originality, this is a valuable book for anyone interested in the subject from other than the purely algebraic point of view. Originally published in 1953. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: David A. Cox Publisher: Springer Science & Business Media ISBN: 1475769113 Category : Mathematics Languages : en Pages : 513
Book Description
An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.
Author: Masayoshi Miyanishi Publisher: American Mathematical Soc. ISBN: 9780821887707 Category : Mathematics Languages : en Pages : 268
Book Description
Students often find, in setting out to study algebraic geometry, that most of the serious textbooks on the subject require knowledge of ring theory, field theory, local rings, and transcendental field extensions, and even sheaf theory. Often the expected background goes well beyond college mathematics. This book, aimed at senior undergraduates and graduate students, grew out of Miyanishi's attempt to lead students to an understanding of algebraic surfaces while presenting thenecessary background along the way. Originally published in Japanese in 1990, it presents a self-contained introduction to the fundamentals of algebraic geometry. This book begins with background on commutative algebras, sheaf theory, and related cohomology theory. The next part introduces schemes andalgebraic varieties, the basic language of algebraic geometry. The last section brings readers to a point at which they can start to learn about the classification of algebraic surfaces.
Author: Ulrich Görtz
Author: Ulrich Görtz
Author: Ulrich Görtz
Author: Steven Dale Cutkosky
Author: Robin Hartshorne
Author: V.I. Danilov
Author: R.K. Lazarsfeld
Author: Igor Rostislavovich Shafarevich
Author: Solomon Lefschetz
Author: David A. Cox
Author: Masayoshi Miyanishi