Caustics of plane curves, their birationality and matrix projections
Algebraic Geometry
2013-06-25 v2 Differential Geometry
Abstract
After recalling the notion of caustics of plane curves and basic equations, we first show the birationality of the caustic map for a general source point S in the plane. Then we prove more generally a theorem for curves D in the projective space of 3x3 symmetric matrices B. For a general 3x1 vector S the projection to the plane given by B --- BS is birational on D, unless D is not a line and D is contained in a plane of the form Delta_v = {B | Bv = 0}.
Keywords
Cite
@article{arxiv.1304.3861,
title = {Caustics of plane curves, their birationality and matrix projections},
author = {Fabrizio Catanese},
journal= {arXiv preprint arXiv:1304.3861},
year = {2013}
}
Comments
10 pages, to appear in a Springer Verlag volume dedicated to Klaus Hulek on the occasion of his 60-th birthday. Final version, added some remarks by the referee