Resolving singularities of curves with one toric morphism

We give an explicit positive answer, in the case of reduced curve singularities, to a question of B. Teissier about the existence of a toric embedded resolution after reembedding. In the case of a curve singularity pC,Oq contained in a non singular surface S such a reembedding may be defined in term...

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Detalles Bibliográficos
Autores: Felipe, Ana Belén de, González Pérez, Pedro Daniel, Mourtada, Hussein
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71921
Acceso en línea:https://hdl.handle.net/20.500.14352/71921
Access Level:acceso abierto
Palabra clave:512.7
Divisorial valuations
Curve singularities
Generating sequences
Resolution of singularities
Toric geometry
Local tropicalization
Torific embedding
Geometria algebraica
1201.01 Geometría Algebraica
Descripción
Sumario:We give an explicit positive answer, in the case of reduced curve singularities, to a question of B. Teissier about the existence of a toric embedded resolution after reembedding. In the case of a curve singularity pC,Oq contained in a non singular surface S such a reembedding may be defined in terms of a sequence of maximal contact curves associated to C. We prove that there exists a toric modification, after reembedding, which provides an embedded resolution of C. We use properties of the semivaluation space of S at O to describe how the the dual graph of the minimal embedded resolution of C may be seen on the local tropicalization of S associated to this reembedding.