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