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arXiv · 1304.3861

Caustics of plane curves, their birationality and matrix projections

Fabrizio Catanese
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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}.

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Fabrizio Catanese. 2013-06-24. Caustics of plane curves, their birationality and matrix projections. https://arxiv.org/abs/1304.3861

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