On caustics by reflection of algebraic surfaces

Alfrederic Josse; Francoise Pene

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arXiv · 1304.3883

On caustics by reflection of algebraic surfaces

Alfrederic Josse·Francoise Pene

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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.

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Alfrederic Josse, Francoise Pene. 2014-06-26. On caustics by reflection of algebraic surfaces. https://arxiv.org/abs/1304.3883

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