  We show the existence of toric resolution tower for an irreducible curve
singularity which is explicitly described by Tschirnhausen polynomials. We
deduce for a smooth affine plane curve from its topology restrictions for its
singularity at infinity. For instance, we discribe the singularities at
infinity (up to equisingular deformation) for curves of genus 0,1 and 2. From
this follows an extension of the Abhyankar-Moh-Suzuki theorem to genus 1 and 2.
