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Joins and intersections /

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

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Bibliographic Details
Main Author: Flenner, H. (Hubert)
Corporate Author: SpringerLink (Online service)
Other Authors: O'Carroll, L. (Liam), Vogel, Wolfgang, 1940-
Format: eBook
Language:English
Published: Berlin ; New York : Springer, [1999]
Series:Springer monographs in mathematics.
Subjects:
Intersection theory (Mathematics)
Commutative algebra.
Geometry, Algebraic.
Algebraic Geometry.
Intersections, Théorie des.
Algèbre commutative.
Géométrie algébrique.
Verzamelingen (wiskunde)
Doorsneden (verzamelingen)
Algèbres commutatives.
Kommutative Algebra.
Algebraische Geometrie.
Schnitttheorie.
Intersection theory.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • 1. The Classical Bezout Theorem. 1.1. Degrees of Projective Schemes. 1.2. Multiplicities of Local Rings. 1.3. Joins. 1.4. The Classical Bezout Theorem. 1.5. Genetic Bertini Theorems
  • 2. The Intersection Algorithm and Applications. 2.1. The Intersection Algorithm. 2.2. Application I: The Refined Bezout Theorem. 2.3. Segre Classes, [upsilon]-Cycles and Positivity. 2.4. Segre Classes: The General Case. 2.5. Limits of Joins and Intersections
  • 3. Connectedness and Bertini Theorems. 3.1. Connectedness Theorems. 3.2. Applications to Intersections and Singularities of Mappings. 3.3. Open Loci Results and the Generic Principle. 3.4. Bertini Theorems. 3.5. Grothendieck's Finiteness Theorem and Applications.