Jet schemes and minimal embedded desingularization of plane branches

Abstract

For a plane branch C with g Puiseux pairs, we determine the irreducible components of its jet schemes which correspond to the star (or rupture) and end divisors that appear on the dual graph of the minimal embedded desingularization of C. We exploit these informations to construct a Teissier type resolution of C embedded in $${\mathbb{C}^{g+1}}$$ , which is special in the sense that its restriction to the strict transform of the plane induces the minimal embedded desingularization of C.