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Author : M. Miyanishi
Publisher : Springer
ISBN 13 : 3540386602
Total Pages : 262 pages
Book Rating : 4.5/5 (43 download)
Download or read book Non-complete Algebraic Surfaces written by M. Miyanishi and published by Springer. This book was released on 2006-11-15 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Masayoshi Miyanishi
Publisher : American Mathematical Soc.
ISBN 13 : 0821805045
Total Pages : 269 pages
Book Rating : 4.8/5 (218 download)
Download or read book Open Algebraic Surfaces written by Masayoshi Miyanishi and published by American Mathematical Soc.. This book was released on 2001 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic background in algebraic geometry. This volume is a continuation of the work presented in the author's previous publication, Algebraic Geometry, Volume 136 in the AMS series, Translations of Mathematical Monographs.
Author : Oscar Zariski
Publisher : Springer Science & Business Media
ISBN 13 : 3642619916
Total Pages : 285 pages
Book Rating : 4.6/5 (426 download)
Download or read book Algebraic Surfaces written by Oscar Zariski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The author's book [...] saw its first edition in 1935. [...] Now as before, the original text of the book is an excellent source for an interested reader to study the methods of classical algebraic geometry, and to find the great old results. [...] a timelessly beautiful pearl in the cultural heritage of mathematics as a whole." Zentralblatt MATH
Author : Masayoshi Miyanishi
Publisher : Springer Verlag
ISBN 13 : 9780387107035
Total Pages : 244 pages
Book Rating : 4.1/5 (7 download)
Download or read book Non-complete Algebraic Surfaces written by Masayoshi Miyanishi and published by Springer Verlag. This book was released on 1981 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David Mumford
Publisher : Princeton University Press
ISBN 13 : 1400882060
Total Pages : 212 pages
Book Rating : 4.4/5 (8 download)
Download or read book Lectures on Curves on an Algebraic Surface. (AM-59), Volume 59 written by David Mumford and published by Princeton University Press. This book was released on 2016-03-02 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
Author : Robert Silhol
Publisher : Springer
ISBN 13 : 3540706496
Total Pages : 226 pages
Book Rating : 4.5/5 (47 download)
Download or read book Real Algebraic Surfaces written by Robert Silhol and published by Springer. This book was released on 2006-11-14 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rick Miranda
Publisher : American Mathematical Soc.
ISBN 13 : 0821802682
Total Pages : 414 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic Curves and Riemann Surfaces written by Rick Miranda and published by American Mathematical Soc.. This book was released on 1995 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Kunihiko Kodaira
Publisher : Springer Nature
ISBN 13 : 9811573808
Total Pages : 86 pages
Book Rating : 4.8/5 (115 download)
Download or read book Theory of Algebraic Surfaces written by Kunihiko Kodaira and published by Springer Nature. This book was released on 2020-09-17 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an English translation of the book in Japanese, published as the volume 20 in the series of Seminar Notes from The University of Tokyo that grew out of a course of lectures by Professor Kunihiko Kodaira in 1967. It serves as an almost self-contained introduction to the theory of complex algebraic surfaces, including concise proofs of Gorenstein's theorem for curves on a surface and Noether's formula for the arithmetic genus. It also discusses the behavior of the pluri-canonical maps of surfaces of general type as a practical application of the general theory. The book is aimed at graduate students and also at anyone interested in algebraic surfaces, and readers are expected to have only a basic knowledge of complex manifolds as a prerequisite.
Author : Kunihiko Kodaira
Publisher : CUP Archive
ISBN 13 : 9780521217774
Total Pages : 424 pages
Book Rating : 4.2/5 (177 download)
Download or read book Complex Analysis and Algebraic Geometry written by Kunihiko Kodaira and published by CUP Archive. This book was released on 1977 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Arnaud Beauville
Publisher : Cambridge University Press
ISBN 13 : 9780521498425
Total Pages : 148 pages
Book Rating : 4.4/5 (984 download)
Download or read book Complex Algebraic Surfaces written by Arnaud Beauville and published by Cambridge University Press. This book was released on 1996-06-28 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Kenji Matsuki
Publisher : Springer Science & Business Media
ISBN 13 : 147575602X
Total Pages : 502 pages
Book Rating : 4.4/5 (757 download)
Download or read book Introduction to the Mori Program written by Kenji Matsuki and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic varieties. The author presents this theory in an easy and understandable way with lots of background motivation. Prerequisites are those covered in Hartshorne's book "Algebraic Geometry." This is the first book in this extremely important and active field of research and will become a key resource for graduate students wanting to get into the area.
Author : Ulf Persson
Publisher : American Mathematical Soc.
ISBN 13 : 082182189X
Total Pages : 164 pages
Book Rating : 4.8/5 (218 download)
Download or read book On Degenerations of Algebraic Surfaces written by Ulf Persson and published by American Mathematical Soc.. This book was released on 1977 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: We will study the relationships between the components of a singular fiber and the non-singular fiber, in a family of surfaces over a disc. Special emphasis will be put on the ties with classification theory of surfaces.
Author : David Mumford
Publisher : Princeton University Press
ISBN 13 : 9780691079936
Total Pages : 224 pages
Book Rating : 4.0/5 (799 download)
Download or read book Lectures on Curves on an Algebraic Surface written by David Mumford and published by Princeton University Press. This book was released on 1966-08-21 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures, delivered by Professor Mumford at Harvard in 1963-1964, are devoted to a study of properties of families of algebraic curves, on a non-singular projective algebraic curve defined over an algebraically closed field of arbitrary characteristic. The methods and techniques of Grothendieck, which have so changed the character of algebraic geometry in recent years, are used systematically throughout. Thus the classical material is presented from a new viewpoint.
Author : Qiang Ye
Publisher :
ISBN 13 :
Total Pages : 200 pages
Book Rating : 4.:/5 (968 download)
Download or read book On Algebraic Surfaces with Non-positive Kodaira Dimension written by Qiang Ye and published by . This book was released on 2001 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Oscar Zariski
Publisher : Springer
ISBN 13 : 3540360921
Total Pages : 109 pages
Book Rating : 4.5/5 (43 download)
Download or read book An Introduction to the Theory of Algebraic Surfaces written by Oscar Zariski and published by Springer. This book was released on 2006-11-14 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : W. Barth
Publisher : Springer Science & Business Media
ISBN 13 : 364296754X
Total Pages : 315 pages
Book Rating : 4.6/5 (429 download)
Download or read book Compact Complex Surfaces written by W. Barth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Introduction. - Standard Notations. - Preliminaries. - Curves on Surfaces. - Mappings of Surfaces. - Some General Properties of Surfaces. - Examples. - The Enriques-Kodaira Classification. - Surfaces of General Type. - K3-Surfaces and Enriques Surfaces. - Bibliography. - Subject Index.
Author : Masayoshi Miyanishi
Publisher : World Scientific
ISBN 13 : 9811215227
Total Pages : 456 pages
Book Rating : 4.8/5 (112 download)
Download or read book Algebraic Surfaces In Positive Characteristics: Purely Inseparable Phenomena In Curves And Surfaces written by Masayoshi Miyanishi and published by World Scientific. This book was released on 2020-06-29 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field. However, over a field of positive characteristics, many unpredictable phenomena arise where analyses will lead to further developments.In the present book, we consider first the forms of the affine line or the additive group, classification of such forms and detailed analysis. The forms of the affine line considered over the function field of an algebraic curve define the algebraic surfaces with fibrations by curves with moving singularities. These fibrations are investigated via the Mordell-Weil groups, which are originally introduced for elliptic fibrations.This is the first book which explains the phenomena arising from purely inseparable coverings and Artin-Schreier coverings. In most cases, the base surfaces are rational, hence the covering surfaces are unirational. There exists a vast, unexplored world of unirational surfaces. In this book, we explain the Frobenius sandwiches as examples of unirational surfaces.Rational double points in positive characteristics are treated in detail with concrete computations. These kinds of computations are not found in current literature. Readers, by following the computations line after line, will not only understand the peculiar phenomena in positive characteristics, but also understand what are crucial in computations. This type of experience will lead the readers to find the unsolved problems by themselves.
