%0 Journal Article 
%A García Barroso, Evelia R.
%A García García, Juan Ignacio
%A Santana Sánchez, Luis José
%A Vigneron Tenorio, Alberto
%T Conductors of Abhyankar-Moh semigroups of even degrees
%D 2023
%@ 2688-1594
%U http://hdl.handle.net/10498/32568
%X 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.
%K Abhyankar-Moh inequality
%K conductor
%K gluing of semigroups
%K branch at infinity
%K Abhyankar-Moh semigroups
%~ Universidad de Cádiz