Monomial generators of complete planar ideals

We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial e...

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Detalles Bibliográficos
Autores: Alberich Carramiñana, Maria|||0000-0003-2749-4875, Álvarez Montaner, Josep|||0000-0001-6793-368X, Blanco Fernández, Guillem|||0000-0002-6073-4175
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/180848
Acceso en línea:https://hdl.handle.net/2117/180848
https://dx.doi.org/10.1142/S0219498821500328
Access Level:acceso abierto
Palabra clave:Algebraic geometry
Commutative algebra
Complete ideals
aximal contact curves
Multiplier ideals
Geometria algebraica
Àlgebra commutativa
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
Descripción
Sumario:We provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements associated to the minimal log-resolution of the ideal. Furthermore, the monomial expression given by our method is an equisingularity invariant of the ideal. As an outcome, we provide a geometric method to compute the integral closure of a planar ideal and we apply our algorithm to some families of complete ideals