On the Resolution Graph of a Plane Curve
Joao Cabral, Orlando Neto, Pedro C. Silva

TL;DR
This paper demonstrates that the resolution graph of a plane curve singularity can be uniquely decomposed into simpler, elementary components, providing a structured understanding of the singularity resolution process.
Contribution
It introduces a canonical decomposition method for the resolution graph of plane curve singularities into elementary graphs, enhancing the structural analysis of singularities.
Findings
Resolution graph admits a canonical decomposition.
Decomposition into elementary graphs is unique.
Provides a new framework for analyzing singularities.
Abstract
We show that the resolution graph of a plane curve singularity admits a canonical decomposition into elementary graphs.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation
