Degree Year

2020

Document Type

Thesis

Degree Name

Bachelor of Arts

Department

Mathematics

Advisor(s)

Susan Jane Colley

Keywords

Algebraic geometry, Mathematics, Curves, Polynomials, Étienne Bézout, Bézout's Theorem, Multiplicities, Multiplicity, Plane curves, Projective geometry, Projective plane curves, Projective space, Intersection, Intersection number, Intersecting curves

Abstract

One area of interest in studying plane curves is intersection. Namely, given two plane curves, we are interested in understanding how they intersect. In this paper, we will build the machinery necessary to describe this intersection. Our discussion will include developing algebraic tools, describing how two curves intersect at a given point, and accounting for points at infinity by way of projective space. With all these tools, we will prove Bézout’s theorem, a robust description of the intersection between two curves relating the degrees of the defining polynomials to the number of points in the intersection.

Included in

Mathematics Commons

Share

COinS