Semigroups corresponding to branches at infinity of coordinate lines in the affine plane

TL;DR

This paper characterizes semigroups associated with branches at infinity of certain affine plane curves, using characteristic sequences, and identifies conditions under which these curves can be transformed into the coordinate axis via polynomial automorphisms.

Contribution

It provides a characterization of semigroups at infinity of affine curves that are equivalent to the coordinate axis through polynomial automorphisms, using characteristic sequences.

Findings

Semigroups at infinity are characterized by specific characteristic sequences.

Conditions are established for when a curve can be transformed into the axis $x=0$.

The results connect semigroup properties with polynomial automorphisms.

Abstract

We characterize in terms of characteristic sequences the semigroups corresponding to branches at infinity of plane affine curves $\Gamma$ for which there exists a polynomial automorphism mapping $\Gamma$ onto the axis $x=0$.