Geometry of plane curves via Tschirnhausen resolution tower
alg-geom
2015-06-30 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.alg-geom/9508007,
title = {Geometry of plane curves via Tschirnhausen resolution tower},
author = {Norbert A'Campo and Mutsuo Oka},
journal= {arXiv preprint arXiv:alg-geom/9508007},
year = {2015}
}
Comments
AMSTex v.2.1, 25 pages with one figure