@article{GARCÍA BARROSO2023, 
author = {Evelia R. GARCÍA BARROSO and Juan Ignacio GARCÍA-GARCÍA and Luis José SANTANA SÁNCHEZ and Alberto VIGNERON-TENORIO},
title = {Conductors of Abhyankar-Moh semigroups of even degrees},
year = {2023},
journal = {Electronic Research Archive},
volume = {31},
number = {4},
pages = {2213-2229},
keywords = {Abhyankar-Moh inequality, Abhyankar-Moh semigroups, conductor, gluing of semigroups, branch at infinity},
url = {https://www.sciopen.com/article/10.3934/era.2023113},
doi = {10.3934/era.2023113},
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, García Barroso and Płoski 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.}
}