KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 47 Issue: 4

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

Muhammad Ahsan Binyamin
Hafız Muhammad Afzal Siddiqui
Amir Shehzad
Sayfa
—
Yayın Tarihi
2018-08-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri: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.
💡
Sonuç & Katkı:The classification shows that the resolution graph of a weighted homogeneous plane curve singularity is always a caterpillar.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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.

🔖

Bu Makaleye Atıf Yap

Binyamin, M. A., Siddiqui, H. 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, Volume: 47 Issue: 4. https://ajindex.com/articles/1402905

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (9)

  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 Pster, G.; Local Analytic Geometry, Vieweg (2000).
  4. Jingen, Y.; Curve Singularities and Graphs, Acta Mathematica Sinica, 6 (1), 87-96, (1990).
  5. Kollár, J.; Lectures on Resolution of Singularities, Princeton University Press (2007).
  6. Kang, C.; Analytic Types of Plane Curve Singularities defined by Weighted Homogeneous Polynomials, Trans. A.M.S. 352 (9), 3995-4006, (2000).
  7. Muhly, H.T. and Zariski, O.; The Resolution of Singularities of an Algebraic curve, Amer.J.Math., 61 (1), 107-114, (1939).
  8. Saito, K.; Quasihomogene isolierte singularitäten von hyperächen, Invent. Math. 14, 123- 142, (1971).
  9. Wall, C.T.C.; Singular Points of Plane Curves, Cambridge University Press (2004).