Embedding of line in the plane and Abhyankar-Moh Epimorphism Theorem
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- Title
- Embedding of line in the plane and Abhyankar-Moh Epimorphism Theorem
- Authors
- Joe, D; Park, H
- Date Issued
- 2009-01
- Publisher
- Korean Mathematical Society
- 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; ENUMERATIVE GEOMETRY; SINGULARITIES; CURVES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/25955
- DOI
- 10.4134/BKMS.2009.46.1.171
- ISSN
- 1015-8634
- Article Type
- Article
- Citation
- BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, vol. 46, no. 1, page. 171 - 182, 2009-01
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