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Conductors of Abhyankar-Moh semigroups of even degrees
- Publication Year :
- 2022
-
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.
- Subjects :
- Mathematics - Algebraic Geometry
Mathematics - Commutative Algebra
20M14, 14H20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2209.04232
- Document Type :
- Working Paper