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| Author | : Arnaud Beauville |
| Publisher | : Cambridge University Press |
| Total Pages | : 148 |
| Release | : 1996-06-28 |
| Genre | : Mathematics |
| ISBN | : 9780521498425 |
Download Complex Algebraic Surfaces Book in PDF, ePub and Kindle
Developed over more than a century, and still an active area of research today, the classification of algebraic surfaces is an intricate and fascinating branch of mathematics. In this book Professor BeauviIle gives a lucid and concise account of the subject, following the strategy of F. Enriques, but expressed simply in the language of modern topology and sheaf theory, so as to be accessible to any budding geometer. This volume is self contained and the exercises succeed both in giving the flavour of the extraordinary wealth of examples in the classical subject, and in equipping the reader with most of the techniques needed for research.
| Author | : W. Barth |
| Publisher | : Springer |
| Total Pages | : 439 |
| Release | : 2015-05-22 |
| Genre | : Mathematics |
| ISBN | : 3642577393 |
Download Compact Complex Surfaces Book in PDF, ePub and Kindle
In the 19 years which passed since the first edition was published, several important developments have taken place in the theory of surfaces. The most sensational one concerns the differentiable structure of surfaces. Twenty years ago very little was known about differentiable structures on 4-manifolds, but in the meantime Donaldson on the one hand and Seiberg and Witten on the other hand, have found, inspired by gauge theory, totally new invariants. Strikingly, together with the theory explained in this book these invariants yield a wealth of new results about the differentiable structure of algebraic surfaces. Other developments include the systematic use of nef-divisors (in ac cordance with the progress made in the classification of higher dimensional algebraic varieties), a better understanding of Kahler structures on surfaces, and Reider's new approach to adjoint mappings. All these developments have been incorporated in the present edition, though the Donaldson and Seiberg-Witten theory only by way of examples. Of course we use the opportunity to correct some minor mistakes, which we ether have discovered ourselves or which were communicated to us by careful readers to whom we are much obliged.
| 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 | : Lucian Badescu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 261 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 147573512X |
Download Algebraic Surfaces Book in PDF, ePub and Kindle
This book presents fundamentals from the theory of algebraic surfaces, including areas such as rational singularities of surfaces and their relation with Grothendieck duality theory, numerical criteria for contractibility of curves on an algebraic surface, and the problem of minimal models of surfaces. In fact, the classification of surfaces is the main scope of this book and the author presents the approach developed by Mumford and Bombieri. Chapters also cover the Zariski decomposition of effective divisors and graded algebras.
| Author | : Kunihiko Kodaira |
| Publisher | : CUP Archive |
| Total Pages | : 424 |
| Release | : 1977 |
| Genre | : Mathematics |
| ISBN | : 9780521217774 |
Download Complex Analysis and Algebraic Geometry Book in PDF, ePub and Kindle
The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.
| Author | : Frances Clare Kirwan |
| Publisher | : Cambridge University Press |
| Total Pages | : 278 |
| Release | : 1992-02-20 |
| Genre | : Mathematics |
| ISBN | : 9780521423533 |
Download Complex Algebraic Curves Book in PDF, ePub and Kindle
This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.
| Author | : Robert Friedman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 532 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662030284 |
Download Smooth Four-Manifolds and Complex Surfaces Book in PDF, ePub and Kindle
In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these "low" dimensions.
| Author | : Robert Friedman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 333 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461216885 |
Download Algebraic Surfaces and Holomorphic Vector Bundles Book in PDF, ePub and Kindle
A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.
| Author | : Donu Arapura |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 326 |
| Release | : 2012-02-15 |
| Genre | : Mathematics |
| ISBN | : 1461418097 |
Download Algebraic Geometry over the Complex Numbers Book in PDF, ePub and Kindle
This is a relatively fast paced graduate level introduction to complex algebraic geometry, from the basics to the frontier of the subject. It covers sheaf theory, cohomology, some Hodge theory, as well as some of the more algebraic aspects of algebraic geometry. The author frequently refers the reader if the treatment of a certain topic is readily available elsewhere but goes into considerable detail on topics for which his treatment puts a twist or a more transparent viewpoint. His cases of exploration and are chosen very carefully and deliberately. The textbook achieves its purpose of taking new students of complex algebraic geometry through this a deep yet broad introduction to a vast subject, eventually bringing them to the forefront of the topic via a non-intimidating style.
| Author | : Ciro Ciliberto |
| Publisher | : |
| Total Pages | : |
| Release | : 2020 |
| Genre | : |
| ISBN | : 9783037192108 |
Download Classification of Complex Algebraic Surfaces Book in PDF, ePub and Kindle
