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Article Dans Une Revue Mathematische Annalen Année : 2023

Resolving singularities of curves with one toric morphism

Résumé

Abstract 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 ( C , O ) contained in a non singular surface S such a reembedding may be defined in terms of a sequence of maximal contact curves of the minimal embedded resolution of 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 dual graph of the minimal embedded resolution of C may be seen on the local tropicalization of S associated to this reembedding.

Dates et versions

hal-04008132 , version 1 (28-02-2023)

Identifiants

Citer

Ana Belén de Felipe, Pedro González Pérez, Hussein Mourtada. Resolving singularities of curves with one toric morphism. Mathematische Annalen, In press, https://link.springer.com/article/10.1007/s00208-022-02504-7. ⟨10.1007/s00208-022-02504-7⟩. ⟨hal-04008132⟩
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