Conductors of Abhyankar-Moh semigroups of even degrees
Algebraic Geometry
2022-09-12 v1 Commutative Algebra
Abstract
In their paper on the embeddings of the line in the plane, Abhyankar and Moh proved an important inequality, now known as the Abhyankar-Moh inequality, which can be stated in terms of the semigroup associated with the branch at infinity of a plane algebraic curve. Barrolleta, Garc\'ia Barroso and P\loski studied the semigroups of integers satisfying the Abhyankar-Moh inequality and call them Abhyankar-Moh semigroups. They described such semigroups with the maximum conductor. In this paper we prove that all possible conductor values are achieved for the Abhyankar-Moh semigroups of even degree. Our proof is constructive, explicitly describing families that achieve a given value as its conductor.
Keywords
Cite
@article{arxiv.2209.04232,
title = {Conductors of Abhyankar-Moh semigroups of even degrees},
author = {Evelia R. GarcÍa Barroso and Juan Ignacio GarcÍa-GarcÍa and Luis José Santana SÁnchez and Alberto Vigneron-Tenorio},
journal= {arXiv preprint arXiv:2209.04232},
year = {2022}
}