Resolving singularities of curves with one toric morphism

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Felipe, Ana Belén de and González Pérez, Pedro Daniel and Mourtada, Hussein (2022) Resolving singularities of curves with one toric morphism. Mathematische Annalen . ISSN 1432-1807

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Official URL: https://doi.org/10.1007/s00208-022-02504-7



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 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.


Item Type:Article
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CRUE-CSIC (Acuerdos Transformativos 2022)

Uncontrolled Keywords:Divisorial valuations, Curve singularities, Generating sequences,Resolution of singularities, Toric geometry, Local tropicalization, Torific embedding
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:74269
Deposited On:01 Sep 2022 11:00
Last Modified:21 Nov 2022 09:54

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