Local trees in the theory of affine plane curves
type: Item
instance of: scholarly article
title: Local trees in the theory of affine plane curves
zbMATH Open document ID: 0758.14018
published in: Journal of Mathematics of Kyoto University
publication date: 1992-09-27T00:00:00Z
review text: Let \(S\) be a complete non singular algebraic surface and \(D\in\text{Div}(S)\) with normal crossing. Then the pair \((S,D)\) determines a weighted graph which carries some information about the surface \(S\backslash D\). If \(D\) does not have normal crossings then one has to blow-up \(S\) at the ``bad'' points of \(D\). In this paper it is developed a graph theory which relates the desingularization process to graph-theoretic devices called ``local trees''. Application of the methods to the classification of birational morphisms of the affine plane with one or two fundamental points is given.
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14C20
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14N10
zbMATH DE Number: 59733
zbMATH Keywords: plane curves
zbMATH Keywords: divisor on algebraic surface
zbMATH Keywords: local trees
zbMATH Keywords: weighted graph
zbMATH Keywords: desingulariztion
author: Daniel Daigle
reviewed by: A. Del Centina
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250519720
OpenAlex ID: W1518075556
DOI: 10.1215/KJM/1250519720
description: scientific article; zbMATH DE number 59733