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ON THE CLASS OF CAUSTICS BY REFLECTION OF PLANAR CURVES

By Alfrederic Josse, Françoise and P Ène

Abstract

Abstract. Given any light position S ∈ 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. the lines containing S) and their reflected lines after reflection on the mirror curve C. The caustic by reflection ΣS(C) is the Zariski closure of the envelope of these reflected lines. We introduce the notion of reflected polar curve and express the class of ΣS(C) in terms of intersection numbers of C with the reflected polar curve, thanks to a fundamental lemma established in [15]. This approach enables us to state an explicit formula for the class of ΣS(C) in every case in terms of intersection numbers of the initial curve C

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.373.1825
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