On the degree of caustics of reflection
Algebraic Geometry
2012-06-21 v2
Abstract
Given a point S and any irreducible algebraic curve C in P^2 (with any type of singularities), we consider the caustic of reflection defined as the Zariski closure of the envelope of the reflected lines from the point S on the curve C. We identify this caustic with the Zariski closure of the image of C by a rational map. Thanks to a general fundamental lemma, we give a formula for the degree of the caustic of reflection in terms of multiplicity numbers of C (or of its branches). Our formula holds in every case. We also give some precisions about Pl\"ucker formulas.
Cite
@article{arxiv.1201.0621,
title = {On the degree of caustics of reflection},
author = {Alfrederic Josse and Francoise Pene},
journal= {arXiv preprint arXiv:1201.0621},
year = {2012}
}
Comments
35 pages, 1 figure