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Author : G. Ellingsrud
Publisher : Cambridge University Press
Page : 354 pages
File Size : 55,5 Mb
Release : 1992-07-30
Category : Mathematics
ISBN : 9780521433525
A volume of papers describing new methods in algebraic geometry.
Author : David Mumford
Publisher : Springer
Page : 210 pages
File Size : 50,9 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015015620209
Author : Jürgen Richter-Gebert
Publisher : Springer Science & Business Media
Page : 571 pages
File Size : 54,5 Mb
Release : 2011-02-04
Category : Mathematics
ISBN : 9783642172861
Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.
Author : Eric Lord
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 47,9 Mb
Release : 2012-12-14
Category : Mathematics
ISBN : 9781447146315
Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods. The analytic approach is based on homogeneous coordinates, and brief introductions to Plücker coordinates and Grassmann coordinates are presented. This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties. The intricate and novel ideas of ‘Donald’ Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter. This book will be appreciated by mathematics students and those wishing to learn more about the subject of geometry. It makes accessible subjects and theorems which are often considered quite complicated and presents them in an easy-to-read and enjoyable manner.
Author : Pierre Samuel
Publisher : Springer
Page : 180 pages
File Size : 54,8 Mb
Release : 1988-09-12
Category : Mathematics
ISBN : UCSC:32106015310342
The purpose of this book is to revive some of the beautiful results obtained by various geometers of the 19th century, and to give its readers a taste of concrete algebraic geometry. A good deal of space is devoted to cross-ratios, conics, quadrics, and various interesting curves and surfaces. The fundamentals of projective geometry are efficiently dealt with by using a modest amount of linear algebra. An axiomatic characterization of projective planes is also given. While the topology of projective spaces over real and complex fields is described, and while the geometry of the complex projective libe is applied to the study of circles and Möbius transformations, the book is not restricted to these fields. Interesting properties of projective spaces, conics, and quadrics over finite fields are also given. This book is the first volume in the Readings in Mathematics sub-series of the UTM. From the reviews: "...The book of P. Samuel thus fills a gap in the literature. It is a little jewel. Starting from a minimal background in algebra, he succeeds in 160 pages in giving a coherent exposition of all of projective geometry. ... one reads this book like a novel. " D.Lazard in Gazette des Mathématiciens#1
Author : Christian Peskine
Publisher : Unknown
Page : 230 pages
File Size : 44,6 Mb
Release : 1996
Category : Functions of complex variables
ISBN : LCCN:94046980
Author : Christian Okonek,Michael Schneider,Heinz Spindler
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 43,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783034801515
These lecture notes are intended as an introduction to the methods of classi?cation of holomorphic vector bundles over projective algebraic manifolds X. To be as concrete as possible we have mostly restricted ourselves to the case X = P . According to Serre (GAGA) the class- n cation of holomorphic vector bundles is equivalent to the classi?cation of algebraic vector bundles. Here we have used almost exclusively the language of analytic geometry. The book is intended for students who have a basic knowledge of analytic and (or) algebraic geometry. Some fundamental results from these ?elds are summarized at the beginning. One of the authors gave a survey in the S ́eminaire Bourbaki 1978 on the current state of the classi?cation of holomorphic vector bundles over P . This lecture then served as the basis for a course of lectures n in G ̈ottingen in the Winter Semester 78/79. The present work is an extended and up-dated exposition of that course. Because of the - troductory nature of this book we have had to leave out some di?cult topics such as the restriction theorem of Barth. As compensation we have appended to each section a paragraph in which historical remarks are made, further results indicated and unsolved problems presented. The book is divided into two chapters. Each chapter is subdivided into several sections which in turn are made up of a number of pa- graphs. Each section is preceded by a short description of its contents.
Author : G. Ellingsrud,C. Peskine,G. Sacchiero,S. A. Stromme
Publisher : Unknown
Page : 352 pages
File Size : 48,9 Mb
Release : 1992
Category : Algebraic varieties
ISBN : 1107366771
A volume of papers describing new methods in algebraic geometry.
Author : B. Moishezon
Publisher : Springer
Page : 238 pages
File Size : 40,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540372769
Author : H.S.M. Coxeter
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461227342
Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.
Author : Christian Peskine
Publisher : Unknown
Page : 454 pages
File Size : 40,6 Mb
Release : 1843
Category : Mathematics
ISBN : UCAL:B4892012
In this introduction to commutative algebra, the author choses a route that leads the reader through the essential ideas, without getting embroiled in technicalities. He takes the reader quickly to the fundamentals of complex projective geometry, requiring only a basic knowledge of linear and multilinear algebra and some elementary group theory. The author divides the book into three parts. In the first, he develops the general theory of noetherian rings and modules. He includes a certain amount of homological algebra, and he emphasizes rings and modules of fractions as preparation for working with sheaves. In the second part, he discusses polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalization lemma and Hilbert's Nullstellensatz, the author introduces affine complex schemes and their morphisms; he then proves Zariski's main theorem and Chevalley's semi-continuity theorem. Finally, the author's detailed study of Weil and Cartier divisors provides a solid background for modern intersection theory. This is an excellent textbook for those who seek an efficient and rapid introduction to the geometric applications of commutative algebra.
Author : Albrecht Beutelspacher,Ute Rosenbaum
Publisher : Cambridge University Press
Page : 272 pages
File Size : 48,8 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521483646
Projective geometry is not only a jewel of mathematics, but has also many applications in modern information and communication science. This book presents the foundations of classical projective and affine geometry as well as its important applications in coding theory and cryptography. It also could serve as a first acquaintance with diagram geometry. Written in clear and contemporary language with an entertaining style and around 200 exercises, examples and hints, this book is ideally suited to be used as a textbook for study in the classroom or on its own.
Author : Geir Ellingsrud,C Peskine,S A Stromme,G Sacchiero,J W S Cassels,Savilian Professor of Geometry N J Hitchin
Publisher : Unknown
Page : 352 pages
File Size : 42,9 Mb
Release : 2014-05-14
Category : Algebraic varieties
ISBN : 1107361869
A volume of papers describing new methods in algebraic geometry.
Author : David M Calderbank,Michael G. Eastwood,Vladimir S. Matveev,Katharina Neusser
Publisher : American Mathematical Society
Page : 137 pages
File Size : 45,6 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470443009
The authors develop in detail the theory of (almost) c-projective geometry, a natural analogue of projective differential geometry adapted to (almost) complex manifolds. The authors realise it as a type of parabolic geometry and describe the associated Cartan or tractor connection. A Kähler manifold gives rise to a c-projective structure and this is one of the primary motivations for its study. The existence of two or more Kähler metrics underlying a given c-projective structure has many ramifications, which the authors explore in depth. As a consequence of this analysis, they prove the Yano–Obata Conjecture for complete Kähler manifolds: if such a manifold admits a one parameter group of c-projective transformations that are not affine, then it is complex projective space, equipped with a multiple of the Fubini-Study metric.
Author : Reinhold Baer
Publisher : Courier Corporation
Page : 338 pages
File Size : 47,9 Mb
Release : 2012-06-11
Category : Mathematics
ISBN : 9780486154664
Geared toward upper-level undergraduates and graduate students, this text establishes that projective geometry and linear algebra are essentially identical. The supporting evidence consists of theorems offering an algebraic demonstration of certain geometric concepts. 1952 edition.