Overview

The central topic of the book is refined Intersection Theory and its applications, the central tool of investigation being the Stuckrad-Vogel Intersection Algorithm, based on the join construction. This algorithm is used to present a general version of Bezout's Theorem, in classical and refined form. Connections with the Intersection Theory of Fulton-MacPherson are treated, using work of van Gastel employing Segre classes. Bertini theorems and Connectedness theorems form another major theme, as do various measures of multiplicity. We mix local algebraic techniques as e.g. the theory of residual intersections with more geometrical methods, and present a wide range of geometrical and algebraic applications and illustrative examples. The book incorporates methods from Commutative Algebra and Algebraic Geometry and therefore it will deepen the understanding of Algebraists in geometrical methods and widen the interest of Geometers in major tools from Commutative Algebra.

Full Product Details

Author:   H. Flenner ,  L. O'Carroll ,  W. Vogel
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 1999
Dimensions:   Width: 15.50cm , Height: 1.60cm , Length: 23.50cm
Weight:   0.486kg
ISBN:  

9783642085628

ISBN 10:   3642085628
Pages:   301
Publication Date:   06 December 2010
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

1. The Classical Bezout Theorem..- 2. The Intersection Algorithm and Applications.- 3. Connectedness and Bertini Theorems.- 4. Joins and Intersections.- 5. Converse to Bezout’s Theorem.- 6. Intersection Numbers and their Properties.- 7. Linkage, Koszul Cohomology and Intersections.- 8. Further Applications.- A. Appendix..- A.1 Some Standard Results from Commutative Algebra.- A.2 Gorenstein Rings.- A.3 Historical Remarks.- Index of Notations.

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