ON THE TANGENT SPACE OF A WEIGHTED HOMOGENEOUS PLANE CURVE SINGULARITY

Let k be a field of characteristic 0. Let l = Spec(k[x,y]/< f >) be a weighted homogeneous plane curve singularity with tangent space pi l: Tl/k -> l. In this article, we study, from a computational point of view, the Zariski closure l(l) of the set of the 1-jets on l which define formal solutions (in F[[t]](2) for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal N-1(l) defining l(l) as a reduced closed subscheme of T-l/k and obtain applications in terms of logarithmic differential operators (in the plane) along l.