ANALYSIS OF THE OFFSET TO A PARABOLA

摘要

Wei Lu has recently constructed a proper rational parameterization for the two-sided offset to a parabola-indicating that this locus, an irreducible curve of degree n = 6, is of genus 0. The theory of algebraic curves then requires that the parabola offset have 1/2(n - 1)(n - 2) = 10 double points. One affine node and six affine cusps are readily identified by geometric arguments; we show that the remaining three double points are accounted for by a non-ordinary double point at infinity, having double points in its first and second neighborhoods. [References: 10]