On Certain Classes of Curve Singularities with Reduced Tangent Cone

We study a class of rational curves with an ordinary singular point, which was introduced in [Geramita and Orecchia, Minimally Generating Ideals Defining Certain Tangent Cones, J. of Algebra 78, No. 1 (1982), 36 – 57]. We find some conditions under which the tangent cone is reduced and we show that the tangent cone is not always reduced. We construct another class of rational curves with an ordinary singular point satisfying the condition required in [Ibid.] and whose tangent cone is always reduced.