Abstract
Classical Intersection Theory (see for example Weil [Wei]) treats the case of proper intersections, where geometrical objects (usually subvarieties of a nonsingular variety) intersect with the expected dimension. In 1984, two books appeared which surveyed and developed work by the individual authors, coworkers and others on a refined version of Intersection Theory, treating the case of possibly improper intersections, where the intersection could have excess dimension. The first, by W. Fulton [Ful1] (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 algebraic manifolds. It represents nowadays the standard approach to Intersection Theory.
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Dedicated to the memory of Wolfgang
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© 1999 Springer-Verlag Berlin Heidelberg
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Flenner, H., O’Carroll, L., Vogel, W. (1999). Introduction. In: Joins and Intersections. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03817-8_1
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DOI: https://doi.org/10.1007/978-3-662-03817-8_1
Publisher Name: Springer, Berlin, Heidelberg
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