Joins and Intersections (Springer Monographs in Mathematics)

Description

The central topic of the book is refined Intersection Theory and its applications, the central tool of investigation being the Stückrad-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.

First Sentence

This initial chapter is devoted to setting in place certain basic pieces of theory which will be used many times throughout the book, and to establishing certain themes in a classical setting which will subsequently be developed more generally.

Subjects

Other Editions

• Joins and Intersections (Springer Monographs in Mathematics)HardcoverSpringer1999-11-12
• Joins and IntersectionspaperbackSpringer2010-12-07
• Joins and IntersectionsSpringer2013-01-01