Blowing Up Plane Curves

ABSTRACT:“Blowups” of curves are the transformation of a curve at a point to a

`new coordinate system, in which x’ = x and y’ = y/x (or slope at that `

point). The result of such a transformation is that for a singularity

with multiple tangent lines, the slopes of the tangent lines become

points on the y’ axis. This allows the tangents at a certain point to be

easily identified. There are several theories about blowups and their

ability to resolve singularities, namely those regarding resolution of

singularities in plane and analytic plane curves