Embeddings of line in the plane and Abhyankar-Moh epimorphism theorem
Bull. Korean Math. Soc. 2009 Vol. 46, No. 1, 171-182
Printed January 1, 2009
Dosang Joe and Hyungju Park
Konkuk University and Korea Institute for Advanced Study
Abstract : In this paper, we consider the parameter space of the rational plane curves with uni-branched singularity. We show that such a parameter space is decomposable into irreducible components which are rational varieties. Rational parametrizations of the irreducible components are given in a constructive way, by a repeated use of Abhyankar-Moh Epimorphism Theorem. We compute an enumerative invariant of this parameter space, and include explicit computational examples to recover some classically-known invariants.
Keywords : embedding of affine line, Abhyankar-Moh epimorphism theorem, enumerative problems, Puiseux pairs
MSC numbers : 14N10, 14Q05, 14R10
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