3 citations · 7 across the 6 of their papers we have counts for
6 papers
On the halphen transform of algebraic space curves
Alfrederic Josse, Françoise Pène
The Halphen transform of a plane curve is the curve obtained by intersecting the tangent lines of the curve with the corresponding polar lines with respect to some conic. This tran…
Normal class and normal lines of algebraic hypersurfaces
Alfrederic Josse, Francoise Pene
We are interested in the normal class of an algebraic hypersurface Z of the complex projective space P^n, that is the number of normal lines to Z passing through a generic point of…
On caustics by reflection of algebraic surfaces
Alfrederic Josse, Francoise Pene
Given a point S (the light position) in P^3 and an algebraic surface Z (the mirror) of P^3, the caustic by reflection of Z from S is the Zariski closure of the envelope of the refl…
Degree and class of caustics by reflection for a generic source
Alfrederic Josse, Francoise Pene
We are interested in the study of caustics by reflection of irreducible algebraic planar curves (in the complex projective plane). We prove the birationality of the caustic map (fo…
On the class of caustics by reflection
Alfrederic Josse, Francoise Pene
Given any light position S in the complex projective plane P^2 and any algebraic curve C of P^2 (with any kind of singularities), we consider the incident lines coming from S (i.e.…
On the degree of caustics of reflection
Alfrederic Josse, Francoise Pene
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…