Algebraic Geometry Ii PDF Download
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| Author | : David Mumford |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2015 |
| Genre | : Algebraic varieties |
| ISBN | : 9789380250809 |
Download Algebraic Geometry II Book in PDF, ePub and Kindle
Several generations of students of algebraic geometry have learned the subject from David Mumford's fabled "Red Book" containing notes of his lectures at Harvard University. This book contains what Mumford had intended to be Volume II. It covers the material in the "Red Book" in more depth with several more topics added.
| 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 | : Bertrand Toën |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 242 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 0821840991 |
Download Homotopical Algebraic Geometry II: Geometric Stacks and Applications Book in PDF, ePub and Kindle
This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties.
| 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 | : Günter Harder |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 376 |
| Release | : 2011-04-21 |
| Genre | : Mathematics |
| ISBN | : 3834881597 |
Download Lectures on Algebraic Geometry II Book in PDF, ePub and Kindle
This second volume introduces the concept of shemes, reviews some commutative algebra and introduces projective schemes. The finiteness theorem for coherent sheaves is proved, here again the techniques of homological algebra and sheaf cohomology are needed. In the last two chapters, projective curves over an arbitrary ground field are discussed, the theory of Jacobians is developed, and the existence of the Picard scheme is proved. Finally, the author gives some outlook into further developments- for instance étale cohomology- and states some fundamental theorems.
| Author | : I.R. Shafarevich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 270 |
| Release | : 2013-11-22 |
| Genre | : Mathematics |
| ISBN | : 3642609252 |
Download Algebraic Geometry II Book in PDF, ePub and Kindle
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.
| Author | : Claire Voisin |
| Publisher | : Cambridge University Press |
| Total Pages | : 362 |
| Release | : 2007-12-20 |
| Genre | : Mathematics |
| ISBN | : 9780521718028 |
Download Hodge Theory and Complex Algebraic Geometry II: Book in PDF, ePub and Kindle
The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. The main results are the generalized Noether-Lefschetz theorems, the generic triviality of the Abel-Jacobi maps, and most importantly, Nori's connectivity theorem, which generalizes the above. The last part deals with the relationships between Hodge theory and algebraic cycles. The text is complemented by exercises offering useful results in complex algebraic geometry. Also available: Volume I 0-521-80260-1 Hardback $60.00 C
| Author | : Kenji Ueno |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 196 |
| Release | : 1999 |
| Genre | : Mathematics |
| ISBN | : 9780821813577 |
Download Algebraic Geometry 2 Book in PDF, ePub and Kindle
Algebraic geometry is built upon two fundamental notions: schemes and sheaves. The theory of schemes was explained in Algebraic Geometry 1: From Algebraic Varieties to Schemes. In this volume, the author turns to the theory of sheaves and their cohomology. A sheaf is a way of keeping track of local information defined on a topological space, such as the local holomorphic functions on a complex manifold or the local sections of a vector bundle. To study schemes, it is useful to study the sheaves defined on them, especially the coherent and quasicoherent sheaves.
| 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 | : 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.
