2012/01/03 by Alfrederic Josse, Josse, Alfrederic, Francoise Pene +1
Mathematics · #14E05 #14H50 #14N05 #14N10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E05 #msc:14H50 #msc:14N05 #msc:14N10
paper · pdf · doi:10.48550/arxiv.1201.0621
35 pages, 1 figure
arxiv created 2012/06/19 · arxiv updated 2012/06/21
Given a point S and any irreducible algebraic curve C in P2 (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 Plücker formulas.