Mathematics Commons^™

Intersection Number Of Plane Curves, Margaret E. Nichols

Honors Papers

In algebraic geometry, seemingly geometric problems can be solved using algebraic techniques. Some of the most basic geometric objects we can study are polynomial curves in the plane. In this paper we focus on the intersections of two curves. We address both the number of times two curves intersect at a given point, counting multiplicity (whatever that means), and the total number of intersections of the curves, again counting multiplicity. The former is known as the intersection number of the curves at the point. This concept, although geometrically motivated, can be described in algebraic terms; it is this relationship which …