The cone of curves associated to a plane configuration
type: Item
instance of: scholarly article
title: The cone of curves associated to a plane configuration
zbMATH Open document ID: 1080.14045
DOI: 10.4171/CMH/5
author: Francisco Monserrat
author: Carlos Galindo
published in: Commentarii Mathematici Helvetici
publication date: 2005-04-18T00:00:00Z
review text: The cone of curves or of effective divisors is a crucial object in modern algebraic geometry. Questions on singularities, morphisms, minimal models, moduli and many others are closely related to the investigation of the this cone for classes of varieties. The paper under review studies the cone of effective divisors of some blow ups of the projective plane. The result is a series of conditions on the polyhedrality of the cone of effective divisors of the blow up of \({\mathbb P^2}\) in valuations centered in a single point \(p\). The results are applied to singularities of plane curves and to low cardinality configurations.
reviewed by: Massimiliano Mella
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14B05
Mathematics Subject Classification ID: 14C99
Mathematics Subject Classification ID: 14E30
Mathematics Subject Classification ID: 14N20
zbMATH DE Number: 2157819
zbMATH Keywords: effective cone
zbMATH Keywords: plane configuration
zbMATH Keywords: singularities
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/cmh/5
OpenAlex ID: W1980294853
description: scientific article; zbMATH DE number 2157819