Joins And Intersections

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Dedicated to the memory of Wolfgang Classical Intersection Theory (see for example Wei! [Wei]) treats the case of proper intersections, where geometrical objects (usually subvarieties of a non singular variety) intersect with the expected dimension. In 1984, two books appeared which surveyed and developed work by the individual authors, co workers and others on a refined version of Intersection Theory, treating the case of possibly improper intersections, where the intersection could have ex cess dimension. The first, by W. Fulton [Full] (recently revised in updated form), used a geometrical theory of deformation to the normal cone, more specifically, deformation to the normal bundle followed by moving the zero section to make the intersection proper; this theory was due to the author together with R. MacPherson and worked generally for intersections on algeb raic manifolds. It represents nowadays the standard approach to Intersection Theory. The second, by W. Vogel [Vogl], employed an algebraic approach to inter sections; although restricted to intersections in projective space it produced an intersection cycle by a simple and natural algorithm, thus leading to a Bezout theorem for improper intersections. It was developed together with J. Stiickrad and involved a refined version of the classical technique ofreduc tion to the diagonal: here one starts with the join variety and intersects with successive hyperplanes in general position, laying aside components which fall into the diagonal and intersecting the residual scheme with the next hyperplane; since all the hyperplanes intersect in the diagonal, the process terminates.

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Genre : Mathematics
Author : H. Flenner
Publisher : Springer Science & Business Media
Release : 2013-06-29
File : 307 Pages
ISBN-13 : 9783662038178


Joins And Intersections

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BOOK EXCERPT:

Dedicated to the memory of Wolfgang Classical Intersection Theory (see for example Wei! [Wei]) treats the case of proper intersections, where geometrical objects (usually subvarieties of a non singular variety) intersect with the expected dimension. In 1984, two books appeared which surveyed and developed work by the individual authors, co workers and others on a refined version of Intersection Theory, treating the case of possibly improper intersections, where the intersection could have ex cess dimension. The first, by W. Fulton [Full] (recently revised in updated form), used a geometrical theory of deformation to the normal cone, more specifically, deformation to the normal bundle followed by moving the zero section to make the intersection proper; this theory was due to the author together with R. MacPherson and worked generally for intersections on algeb raic manifolds. It represents nowadays the standard approach to Intersection Theory. The second, by W. Vogel [Vogl], employed an algebraic approach to inter sections; although restricted to intersections in projective space it produced an intersection cycle by a simple and natural algorithm, thus leading to a Bezout theorem for improper intersections. It was developed together with J. Stiickrad and involved a refined version of the classical technique ofreduc tion to the diagonal: here one starts with the join variety and intersects with successive hyperplanes in general position, laying aside components which fall into the diagonal and intersecting the residual scheme with the next hyperplane; since all the hyperplanes intersect in the diagonal, the process terminates.

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Genre : Mathematics
Author : H. Flenner
Publisher : Springer Science & Business Media
Release : 1999-10-08
File : 322 Pages
ISBN-13 : 3540663193


Methods Of Algebraic Geometry

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Genre :
Author : William Vallance Douglas Hodge
Publisher : CUP Archive
Release : 1947
File : 456 Pages
ISBN-13 :


Mathematical Frameworks For Component Software Models For Analysis And Synthesis

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The range of components technology is both wide and diverse, but some common understanding is emerging through the ideas of model-based development. These include the notions of interfaces, contracts, services, connectors and architectures. Key issues in the application of the technology are becoming clearer, including the consistent integration of different views of a component, component composition, component coordination and transformation for platforms. However, we still know little about theories that support analysis and synthesis of component-based systems. The distinct feature of this volume is its focus on mathematical models that identify the “core” concepts as first class modeling elements, and its providing of techniques for integrating and relating them. The volume contains eleven chapters by well-established researchers writing from different perspectives. Each chapter gives explicit definitions of components in terms of a set of key aspects and addresses some of the problems of integration and analysis of various views: component specification, component composition, component coordination, refinement and substitution, and techniques for solving problems. The concepts and techniques are motivated and explained with the help of examples and case studies.

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Genre : Computers
Author : Zhiming Liu
Publisher : World Scientific
Release : 2006-11-29
File : 368 Pages
ISBN-13 : 9789814477086


A Collection Of Problems And Theorems With Hints Results And Occasional Solutions Forming Examples In The Methods Of Modern Geometry

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Genre : Coordinates, Trilinear
Author : Robert Henry Wright
Publisher :
Release : 1865
File : 160 Pages
ISBN-13 : BL:A0018174931


An Elementary Course Of Plane Geometry

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Genre : Geometry, Plane
Author : Richard Wormell
Publisher :
Release : 1870
File : 300 Pages
ISBN-13 : BL:A0018173504


Expert Mysql

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MySQL remains one of the hottest open source database technologies. As the database has evolved into a product competitive with proprietary counterparts like Oracle and IBM DB2, MySQL has found favor with large scale corporate users who require high-powered features and performance. Expert MySQL is the first book to delve deep into the MySQL architecture, showing users how to make the most of the database through creation of custom storage handlers, optimization of MySQL's query execution, and use of the embedded server product. This book will interest users deploying MySQL in high-traffic environments and in situations requiring minimal resource allocation.

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Genre : Computers
Author : Charles Bell
Publisher : Apress
Release : 2007-04-01
File : 601 Pages
ISBN-13 : 9781430203469


The School Edition Euclid S Elements Books 1 6 By R Potts Corrected And Enlarged

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Genre :
Author :
Publisher :
Release : 1850
File : 362 Pages
ISBN-13 : BL:A0018180250


Methods Of Algebraic Geometry Book 1 Algebraic Preliminaries Book 2 Projective Space

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Genre : Geometry, Algebraic
Author : William Vallance Douglas Hodge
Publisher :
Release : 1947
File : 454 Pages
ISBN-13 : MINN:319510004769053


Abdominal Wall Hernias

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Abdominal Wall Hernias is the most up-to-date, comprehensive reference available on all aspects of hernia repair. It includes state-of-the-art approaches to conventional open repairs using tissue-to-tissue techniques, the use of prosthetic mesh, minimally invasive approaches, the repair of recurrent and massive hernias, pertinent anatomy, basic science, and emerging biomaterials. The authors present a full spectrum of procedures to enable readers to gain a broad knowledge of the multifaceted repair of hernias. Richly illustrated, this book is a vital resource for all general surgeons and surgeons-in-training.

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Genre : Medical
Author : Robert Bendavid
Publisher : Springer Science & Business Media
Release : 2001-04-20
File : 860 Pages
ISBN-13 : 0387950044