Conductors of Abhyankar-Moh semigroups of even degrees

Autor:	Evelia R. GARCÍA BARROSO, Juan Ignacio GARCÍA-GARCÍA, Luis José SANTANA SÁNCHEZ, Alberto VIGNERON-TENORIO
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	abhyankar-moh inequality abhyankar-moh semigroups conductor gluing of semigroups branch at infinity Mathematics QA1-939 Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Electronic Research Archive, Vol 31, Iss 4, Pp 2213-2229 (2023)
Druh dokumentu:	article
ISSN:	2688-1594
DOI:	10.3934/era.2023113?viewType=HTML
Popis:	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.
Databáze:	Directory of Open Access Journals
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