Editing Intersection number (section)

{{Short description|Generalized notion of counting curve intersections}}
{{about|algebraic geometry|the concept in graph theory|Intersection number (graph theory)}}
In [[mathematics]], and especially in [[algebraic geometry]], the '''intersection number''' generalizes the intuitive notion of counting the number of times two curves intersect to higher dimensions, multiple (more than 2) curves, and accounting properly for [[tangent|tangency]]. One needs a definition of intersection number in order to state results like [[Bézout's theorem]].

The intersection number is obvious in certain cases, such as the intersection of the ''x''- and ''y''-axes in a plane, which should be one. The complexity enters when calculating intersections at points of tangency, and intersections which are not just points, but have higher dimension. For example, if a plane is tangent to a surface along a line, the intersection number along the line should be at least two. These questions are discussed systematically in [[intersection theory]].