English

On caustics by reflection of algebraic surfaces

Algebraic Geometry 2014-06-27 v2

Abstract

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 reflected lines got by reflection of the incident lines (Sm) on Z at m in Z. We use the ramification method to identify the caustic by reflection with the Zariski closure of the image, by a rational map, of an algebraic 2-covering space of Z. We also give a general formula for the degree (with multiplicity) of caustics (by reflection) of algebraic surfaces.

Keywords

Cite

@article{arxiv.1304.3883,
  title  = {On caustics by reflection of algebraic surfaces},
  author = {Alfrederic Josse and Francoise Pene},
  journal= {arXiv preprint arXiv:1304.3883},
  year   = {2014}
}

Comments

31 pages, 9 figures

R2 v1 2026-06-21T23:59:16.477Z