Intersection of algebraic space curves

Abstract

Bezout's theorem gives the degree of intersection of two properly intersecting algebraic varieties. As two irreducible algebraic space curves never intersect properly, Bezout's theorem cannot be directly used to bound the number of intersections of such curves. A general technique is developed in this paper for bounding the maximum number of intersection points of two irreducible space curves. The bound derived is a function of only the degrees of the respective curves. A number of special cases of this intersection problem for low degree curves are studied in some detail.