Joins and intersections Joins and Intersections Springer Monographs in Mathematics Joins and Intersections Copyright Table of Contents Introduction Notations 1. The Classical Bezout Theorem 2. The Intersection Algorithm and Applications 3. Connectedness and Bertini Theorems 4. Joins and Intersections 5. Converse to Bezouts Theorem 6. Intersection Numbers and their Properties 7. Linkage Koszul Cohomology and Intersections 8. Further Applications A. Appendix Bibliography Index of Notations Index. 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 Bezouts 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.