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Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 4

A combinatorial approach to the classification of resolution graphs of weighted homogeneous plane curve singularities

Muhammad Ahsan BİNYAMİN
Ha fız Muhammad Afzal Siddiqui
Amir SHEHZAD
Pages
805–812
Publication Date
2018-08-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The classification shows that the resolution graph of a weighted homogeneous plane curve singularity is always a caterpillar.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:The classification shows that the resolution graph of a weighted homogeneous plane curve singularity is always a caterpillar.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Plane Curves · Weights · Caterpillar

Abstract

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.

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Cite This Article

BİNYAMİN, M. A., Siddiqui, H. F. M. A., SHEHZAD, A. (2018). A combinatorial approach to the classification of resolution graphs of weighted homogeneous plane curve singularities. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 4, 805–812. https://ajindex.com/articles/669438

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References (8)

  1. Arnold, V. I.; Gusein-Zade, S. M.; Varchenko,A. N. Singularities of Differentiable Maps, Volume I, Birkhäuser, Boston Basel Berlin (1985).
  2. Cutkosky, S. D. and Srinivasan, H.; The algebraic fundamental group of a curve singularity, Journal of Algebra 230, 101-126, (2000).
  3. De Jong, T. and P ster, G.; Local Analytic Geometry, Vieweg (2000).
  4. 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).
  5. Kang, C.; Analytic Types of Plane Curve Singularities defi ned by Weighted Homogeneous Polynomials, Trans. A.M.S. 352 (9), 3995-4006, (2000).
  6. Muhly, H.T. and Zariski, O.; The Resolution of Singularities of an Algebraic curve, Amer.J.Math., 61 (1), 107-114, (1939).
  7. Saito, K.; Quasihomogene isolierte singularitäten von hyper ächen, Invent. Math. 14, 123- 142, (1971).
  8. Wall, C.T.C.; Singular Points of Plane Curves, Cambridge University Press (2004).