Classification of Rational Unicuspidal Projective Curves whose Singularities Have one Puiseux Pair
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It is a very old and interesting open problem to characterize those collections of embedded topological types of local plane curve singularities which may appear as singularities of a projective plane curve C of degree d. The goal of the present article is to give a complete (topological) classification of those cases when C is rational and it has a unique singularity which is locally irreducible (i.e., C is unicuspidal) with one Puiseux pair.
KeywordsCuspidal rational plane curves logarithmic Kodaira dimension
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- Fernández de Bobadilla J., Luengo I., Melle-Hernández A., Némethi A.: On rational cuspidal curves, open surfaces and local singularities, arXiv.math.AG/0604421.Google Scholar
- Fujita, T.: On the topology of non-complete algebraic surfaces, J. Fac. Sci. Univ. Tokyo (Ser1A), 29 (1982), 503–566.Google Scholar
- Tono, K.: On rational unicuspidal plane curves with logarithmic Kodaira dimension one, preprint.Google Scholar
- Tsunoda, Sh.: The complements of projective plane curves, RIMS-Kôkyûroku, 446 (1981), 48–56.Google Scholar
- Varchenko, A.N.: On the change of discrete characteristics of critical points of functions under deformations, Uspekhi Mat. Nauk, 38:5 (1985), 126–127.Google Scholar
- Wall, C.T.C.: Singular Points of Plane Curves, London Math. Soc. Student Texts 63, Cambridge University Press, 2004.Google Scholar