@misc{10498/32568,
year = {2023},
url = {http://hdl.handle.net/10498/32568},
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´ıa 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.},
publisher = {American Mathematical Society},
keywords = {Abhyankar-Moh inequality},
keywords = {conductor},
keywords = {gluing of semigroups},
keywords = {branch at infinity},
keywords = {Abhyankar-Moh semigroups},
title = {Conductors of Abhyankar-Moh semigroups of even degrees},
doi = {10.3934/ERA.2023113},
author = {García Barroso, Evelia R. and García García, Juan Ignacio and Santana Sánchez, Luis José and Vigneron Tenorio, Alberto},
}