Topics In The Geometry Of Projective Space

Author : R. Lazarsfeld,Ven
Publisher : Birkhäuser
Page : 51 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783034893480

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Topics in the Geometry of Projective Space by R. Lazarsfeld,Ven Pdf

The main topics discussed at the D. M. V. Seminar were the connectedness theorems of Fulton and Hansen, linear normality and subvarieties of small codimension in projective spaces. They are closely related; thus the connectedness theorem can be used to prove the inequality-part of Hartshorne's conjecture on linear normality, whereas Deligne's generalisation of the connectedness theorem leads to a refinement of Barth's results on the topology of varieties with small codimension in a projective space. The material concerning the connectedness theorem itself (including the highly surprising application to tamely ramified coverings of the projective plane) can be found in the paper by Fulton and the first author: W. Fulton, R. Lazarsfeld, Connectivity and its applications in algebraic geometry, Lecture Notes in Math. 862, p. 26-92 (Springer 1981). It was never intended to be written out in these notes. As to linear normality, the situation is different. The main point was an exposition of Zak's work, for most of which there is no reference but his letters. Thus it is appropriate to take an extended version of the content of the lectures as the central part of these notes.

Author : R. Lazarsfeld
Publisher : Unknown
Page : 56 pages
File Size : 45,6 Mb
Release : 1984-01-01
Category : Electronic
ISBN : 3034893493

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Topics in the Geometry of Projective Space by R. Lazarsfeld Pdf

Author : P. F. Lazarsfeld
Publisher : Birkhauser
Page : 52 pages
File Size : 44,7 Mb
Release : 1985-01-01
Category : Electronic
ISBN : 0817616608

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Topics in the Geometry of Projective Space by P. F. Lazarsfeld Pdf

Author : Igor Rostislavovich Shafarevich
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 49,5 Mb
Release : 1994
Category : Mathematics
ISBN : 3540575545

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Basic Algebraic Geometry 2 by Igor Rostislavovich Shafarevich Pdf

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 : Charles Eugene Springer
Publisher : Unknown
Page : 322 pages
File Size : 55,9 Mb
Release : 1964
Category : Geometry, Analytic
ISBN : UOM:39015049391850

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Geometry and Analysis of Projective Spaces by Charles Eugene Springer Pdf

Author : Christian Okonek,Michael Schneider,Heinz Spindler
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 46,8 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783034801515

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Vector Bundles on Complex Projective Spaces by Christian Okonek,Michael Schneider,Heinz Spindler Pdf

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 : Johannes Ueberberg
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 54,6 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9783642209727

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Foundations of Incidence Geometry by Johannes Ueberberg Pdf

Incidence geometry is a central part of modern mathematics that has an impressive tradition. The main topics of incidence geometry are projective and affine geometry and, in more recent times, the theory of buildings and polar spaces. Embedded into the modern view of diagram geometry, projective and affine geometry including the fundamental theorems, polar geometry including the Theorem of Buekenhout-Shult and the classification of quadratic sets are presented in this volume. Incidence geometry is developed along the lines of the fascinating work of Jacques Tits and Francis Buekenhout. The book is a clear and comprehensible introduction into a wonderful piece of mathematics. More than 200 figures make even complicated proofs accessible to the reader.

Author : R. J. Mihalek
Publisher : Academic Press
Page : 232 pages
File Size : 54,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483265209

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Projective Geometry and Algebraic Structures by R. J. Mihalek Pdf

Projective Geometry and Algebraic Structures focuses on the relationship of geometry and algebra, including affine and projective planes, isomorphism, and system of real numbers. The book first elaborates on euclidean, projective, and affine planes, including axioms for a projective plane, algebraic incidence bases, and self-dual axioms. The text then ponders on affine and projective planes, theorems of Desargues and Pappus, and coordination. Topics include algebraic systems and incidence bases, coordinatization theorem, finite projective planes, coordinates, deletion subgeometries, imbedding theorem, and isomorphism. The publication examines projectivities, harmonic quadruples, real projective plane, and projective spaces. Discussions focus on subspaces and dimension, intervals and complements, dual spaces, axioms for a projective space, ordered fields, completeness and the real numbers, real projective plane, and harmonic quadruples. The manuscript is a dependable reference for students and researchers interested in projective planes, system of real numbers, isomorphism, and subspaces and dimensions.

Author : Eric Lord
Publisher : Springer Science & Business Media
Page : 184 pages
File Size : 54,5 Mb
Release : 2012-12-14
Category : Mathematics
ISBN : 9781447146315

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Symmetry and Pattern in Projective Geometry by Eric Lord Pdf

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 : Evgueni A. Tevelev
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 44,6 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783540269571

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Projective Duality and Homogeneous Spaces by Evgueni A. Tevelev Pdf

Projective duality is a very classical notion naturally arising in various areas of mathematics, such as algebraic and differential geometry, combinatorics, topology, analytical mechanics, and invariant theory, and the results in this field were until now scattered across the literature. Thus the appearance of a book specifically devoted to projective duality is a long-awaited and welcome event. Projective Duality and Homogeneous Spaces covers a vast and diverse range of topics in the field of dual varieties, ranging from differential geometry to Mori theory and from topology to the theory of algebras. It gives a very readable and thorough account and the presentation of the material is clear and convincing. For the most part of the book the only prerequisites are basic algebra and algebraic geometry. This book will be of great interest to graduate and postgraduate students as well as professional mathematicians working in algebra, geometry and analysis.

Author : A. Heyting
Publisher : Elsevier
Page : 160 pages
File Size : 53,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483259314

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Axiomatic Projective Geometry by A. Heyting Pdf

Bibliotheca Mathematica: A Series of Monographs on Pure and Applied Mathematics, Volume V: Axiomatic Projective Geometry, Second Edition focuses on the principles, operations, and theorems in axiomatic projective geometry, including set theory, incidence propositions, collineations, axioms, and coordinates. The publication first elaborates on the axiomatic method, notions from set theory and algebra, analytic projective geometry, and incidence propositions and coordinates in the plane. Discussions focus on ternary fields attached to a given projective plane, homogeneous coordinates, ternary field and axiom system, projectivities between lines, Desargues' proposition, and collineations. The book takes a look at incidence propositions and coordinates in space. Topics include coordinates of a point, equation of a plane, geometry over a given division ring, trivial axioms and propositions, sixteen points proposition, and homogeneous coordinates. The text examines the fundamental proposition of projective geometry and order, including cyclic order of the projective line, order and coordinates, geometry over an ordered ternary field, cyclically ordered sets, and fundamental proposition. The manuscript is a valuable source of data for mathematicians and researchers interested in axiomatic projective geometry.

Author : Mauro Beltrametti
Publisher : European Mathematical Society
Page : 512 pages
File Size : 44,8 Mb
Release : 2009
Category : Mathematics
ISBN : 3037190647

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Lectures on Curves, Surfaces and Projective Varieties by Mauro Beltrametti Pdf

This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students in the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses at the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.

Author : Charles E. Springer
Publisher : Unknown
Page : 299 pages
File Size : 48,7 Mb
Release : 1984
Category : Electronic
ISBN : OCLC:1067619747

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GEOMETRY AND ANALYSIS OF PROJECTIVE SPACES by Charles E. Springer Pdf

Author : Albrecht Beutelspacher,Ute Rosenbaum
Publisher : Cambridge University Press
Page : 272 pages
File Size : 40,7 Mb
Release : 1998-01-29
Category : Mathematics
ISBN : 0521483646

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Projective Geometry by Albrecht Beutelspacher,Ute Rosenbaum Pdf

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 : Peter Jephson Cameron
Publisher : Unknown
Page : 162 pages
File Size : 41,9 Mb
Release : 1992
Category : Geometry, Affine
ISBN : UOM:39015033103568

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Projective and Polar Spaces by Peter Jephson Cameron Pdf