关于反射焦散度
On the degree of caustics of reflection
摘要：
给定一点S和P ^2中的任何不可约代数曲线C（具有任何类型的奇点），我们考虑反射焦散，它被定义为曲线C上从点S反射的线的包络的Zebriki闭包。我们确定这个焦散线与Zubalki封闭的图像的C的一个合理的地图。由于一般的基本引理，我们给出了一个公式的焦散反射的程度方面的多重数的C（或其分支）。我们的公式适用于任何情况。我们也给出了Plücker公式的一些精确性。
英文摘要：
Given a point S and any irreducible algebraic curve C in P^2 (with any type of singularities), we consider the caustic of reflection defined as the Zariski closure of the envelope of the reflected lines from the point S on the curve C. We identify this caustic with the Zariski closure of the image of C by a rational map. Thanks to a general fundamental lemma, we give a formula for the degree of the caustic of reflection in terms of multiplicity numbers of C (or of its branches). Our formula holds in every case. We also give some precisions about Plücker formulas.
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