A combinatorial approach to the classification of resolution graphs of weighted homogeneous plane curve singularities
A combinatorial approach to the classification of resolution graphs of weighted homogeneous plane curve singularities
In this article we describe the classification of the resolution graphs of weighted homogeneous plane curve singularities in terms of their weights by using the concepts of graph theory and combinatorics. The classification shows that the resolution graph of a weighted homogeneous plane curve singularity is always a caterpillar.
Keywords:
Plane Curves, Weights, Caterpillar,
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- Arnold, V. I.; Gusein-Zade, S. M.; Varchenko,A. N. Singularities of Differentiable Maps, Volume I, Birkhäuser, Boston Basel Berlin (1985).
- Cutkosky, S. D. and Srinivasan, H.; The algebraic fundamental group of a curve singularity, Journal of Algebra 230, 101-126, (2000).
- De Jong, T. and P ster, G.; Local Analytic Geometry, Vieweg (2000).
- Jingen, Y.; Curve Singularities and Graphs, Acta Mathematica Sinica, 6 (1), 87-96, (1990).
- Kollár, J.; Lectures on Resolution of Singularities, Princeton University Press (2007).
- Kang, C.; Analytic Types of Plane Curve Singularities defi ned by Weighted Homogeneous Polynomials, Trans. A.M.S. 352 (9), 3995-4006, (2000).
- Muhly, H.T. and Zariski, O.; The Resolution of Singularities of an Algebraic curve, Amer.J.Math., 61 (1), 107-114, (1939).
- Saito, K.; Quasihomogene isolierte singularitäten von hyper ächen, Invent. Math. 14, 123- 142, (1971).
- Wall, C.T.C.; Singular Points of Plane Curves, Cambridge University Press (2004).
- Yayın Aralığı: Yılda 6 Sayı
- Başlangıç: 2002
- Yayıncı: Hacettepe Üniversitesi Fen Fakultesi
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