Conchoidal transform of two plane curves

Details Conchoidal transform of two plane curves Conchoidal transform of two plane curves

2009-05-20

arxiv.org/abs/0905.3255v2

Mathematics

Algebraic Geometry

18 pages Revised version: slight title change, improved exposition, fixed proof of Theorem 5.3 Accepted for publication in App

Scientific paper

The conchoid of a plane curve $C$ is constructed using a fixed circle $B$ in the affine plane. We generalize the classical definition so that we obtain a conchoid from any pair of curves $B$ and $C$ in the projective plane. We present two definitions, one purely algebraic through resultants and a more geometric one using an incidence correspondence in $\PP^2 \times \PP^2$. We prove, among other things, that the conchoid of a generic curve of fixed degree is irreducible, we determine its singularities and give a formula for its degree and genus. In the final section we return to the classical case: for any given curve $C$ we give a criterion for its conchoid to be irreducible and we give a procedure to determine when a curve is the conchoid of another.

Affiliated with

Also associated with

No associations

Rating

Conchoidal transform of two plane curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Conchoidal transform of two plane curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conchoidal transform of two plane curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-242459