Overview
- Authors:
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Hubert Flenner
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Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany
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Liam O’Carroll
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Department of Mathematics and Statistics, University of Edinburgh, Edinburgh, United Kingdom
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Wolfgang Vogel
- The book starts with a new approach to the theory of multiplicities.
- It contains as a central topic the Stückrad- Vogel Algorithm and its interpretation in terms of Segre classes.
- Using the join construction, a proof of Bezout's theorem is given.
- The theme of Bertini and connectedness theorems is investigated.
- Moreover, the theory of residual intersections is fully developed.
- Includes supplementary material: sn.pub/extras
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Table of contents (9 chapters)
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 1-5
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 7-42
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 43-81
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 83-122
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 123-170
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 171-191
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 193-207
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 209-249
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- Hubert Flenner, Liam O’Carroll, Wolfgang Vogel
Pages 251-275
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Back Matter
Pages 277-307
About this book
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.
Authors and Affiliations
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Fakultät für Mathematik, Ruhr-Universität Bochum, Bochum, Germany
Hubert Flenner
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Department of Mathematics and Statistics, University of Edinburgh, Edinburgh, United Kingdom
Liam O’Carroll
