Full paper in PDF format:

$%P. G. Wightwick, Semi-group conditions for affine algebraic plane curves with more than
one
place
at infinity, Rev. Mat. Complut. 20 (2007), no. 1, 139–206. %$

Semi-group Conditions for Affine Algebraic
Plane Curves with More than One Place
at Infinity

Penelope G. WIGHTWICK

Department of Mathematics and Statistics

University of Melbourne

Victoria 3010 — Australia

P.Wightwick@ms.unimelb.edu.au

University of Melbourne

Victoria 3010 — Australia

P.Wightwick@ms.unimelb.edu.au

Accepted: September 28, 2006

ABSTRACT

An interesting and open question is the classification of affine algebraic plane curves. Abhyankar and Moh (1977) completely described the possible links at infinity for those curves where the link has just one component, a knot. Such curves are said to have one place at infinity. The Abhyankar-Moh result has been of great assistance in classifying those polynomials which define a connected curve with one place at infinity. This paper provides a new proof of the Abhyankar-Moh result which is then used to find a description for the case where the polynomial defines a curve with one point at infinity.

Key words: affine algebraic curves, classification, link at infinity.

2000 Mathematics Subject Classification: 14R05 (14H20).