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The valuative tree is the projective limit of Eggers-Wall trees

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The valuative tree is the projective limit of Eggers-Wall trees
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16
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Release Date2018
LanguageEnglish

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Abstract
I will speak about a common work with García Barroso and González P\'erez. Favre and Jonsson described in 2004 from various viewpoints a structure of real tree on the projectified space of semivaluations centered at a smooth point of a complex surface. We describe it from another viewpoint, as the projective limit of the Eggers-Wall trees of the reduced germs of curves at the given point. The Eggers-Wall tree measures the contacts between the various Newton-Puiseux series of a given curve singularity. Therefore, our viewpoint is adapted whenever one studies the local geometry of surfaces using such series.