[PDF] Projective Duality And Homogeneous Spaces eBook

Author : Evgueni A. Tevelev
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 17,1 MB
Release : 2006-03-30
Category : Mathematics
ISBN : 3540269576

GET BOOK

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 : Albrecht Beutelspacher
Publisher : Cambridge University Press
Page : 272 pages
File Size : 47,34 MB
Release : 1998-01-29
Category : Mathematics
ISBN : 9780521483643

GET BOOK

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 : Jorge Stolfi
Publisher : Academic Press
Page : 246 pages
File Size : 31,92 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483265196

GET BOOK

Oriented Projective Geometry: A Framework for Geometric Computations proposes that oriented projective geometry is a better framework for geometric computations than classical projective geometry. The aim of the book is to stress the value of oriented projective geometry for practical computing and develop it as a rich, consistent, and effective tool for computer programmers. The monograph is comprised of 20 chapters. Chapter 1 gives a quick overview of classical and oriented projective geometry on the plane, and discusses their advantages and disadvantages as computational models. Chapters 2 through 7 define the canonical oriented projective spaces of arbitrary dimension, the operations of join and meet, and the concept of relative orientation. Chapter 8 defines projective maps, the space transformations that preserve incidence and orientation; these maps are used in chapter 9 to define abstract oriented projective spaces. Chapter 10 introduces the notion of projective duality. Chapters 11, 12, and 13 deal with projective functions, projective frames, relative coordinates, and cross-ratio. Chapter 14 tells about convexity in oriented projective spaces. Chapters 15, 16, and 17 show how the affine, Euclidean, and linear vector spaces can be emulated with the oriented projective space. Finally, chapters 18 through 20 discuss the computer representation and manipulation of lines, planes, and other subspaces. Computer scientists and programmers will find this text invaluable.

Author : Pierre Samuel
Publisher : Springer
Page : 180 pages
File Size : 35,90 MB
Release : 1988-09-12
Category : Mathematics
ISBN :

GET BOOK

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 : Nicholas Young
Publisher : Cambridge University Press
Page : 327 pages
File Size : 48,82 MB
Release : 2007-01-18
Category : Mathematics
ISBN : 0521691826

GET BOOK

A collection of survey articles by leading young researchers, showcasing the vitality of Russian mathematics.

Author : Mark Nixon
Publisher : Elsevier
Page : 423 pages
File Size : 27,44 MB
Release : 2008-01-08
Category : Computers
ISBN : 0080556728

GET BOOK

Whilst other books cover a broad range of topics, Feature Extraction and Image Processing takes one of the prime targets of applied computer vision, feature extraction, and uses it to provide an essential guide to the implementation of image processing and computer vision techniques. Acting as both a source of reference and a student text, the book explains techniques and fundamentals in a clear and concise manner and helps readers to develop working techniques, with usable code provided throughout. The new edition is updated throughout in line with developments in the field, and is revised to focus on mathematical programming in Matlab. Essential reading for engineers and students working in this cutting edge field Ideal module text and background reference for courses in image processing and computer vision

Author : Lionel J. Mason
Publisher : Oxford University Press
Page : 384 pages
File Size : 33,35 MB
Release : 1996
Category : Language Arts & Disciplines
ISBN : 9780198534983

GET BOOK

Many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection. For example, the Korteweg-de Vries and non-linear Schrodinger equations are reductions of the self-dual Yang-Mills equation. This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It supports two central theories: that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and that twistor theory provides a uniform geometric framework for the study of Backlund transformations, the inverse scattering method, and other such general constructions of integrability theory. The book will be useful to researchers and graduate students in mathematical physics.

Author : Laurentiu Paunescu
Publisher : World Scientific
Page : 475 pages
File Size : 34,16 MB
Release : 2007
Category : Mathematics
ISBN : 9812706895

GET BOOK

The modern theory of singularities provides a unifying theme that runs through fields of mathematics as diverse as homological algebra and Hamiltonian systems. It is also an important point of reference in the development of a large part of contemporary algebra, geometry and analysis. Presented by internationally recognized experts, the collection of articles in this volume yields a significant cross-section of these developments. The wide range of surveys includes an authoritative treatment of the deformation theory of isolated complex singularities by prize-winning researcher K Miyajima. Graduate students and even ambitious undergraduates in mathematics will find many research ideas in this volume and non-experts in mathematics can have an overview of some classic and fundamental results in singularity theory. The explanations are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to go further into the subject and explore the research literature.

Author : Anton Alekseev
Publisher : Springer Nature
Page : 652 pages
File Size : 29,87 MB
Release : 2022-02-05
Category : Mathematics
ISBN : 3030781488

GET BOOK

Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.