An Introduction to Local Tropicalization

Patrick Popescu-Pampu () and Dmitry Stepanov ()
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Patrick Popescu-Pampu: University of Lille, CNRS, UMR 8524 - Laboratoire Paul Painlevé
Dmitry Stepanov: Department of Higher Mathematics and Center of Fundamental Mathematics, Moscow Institute of Physics and Technology

Chapter Chapter 3 in Handbook of Geometry and Topology of Singularities VIII, 2026, pp 103-143 from Springer

Abstract: Abstract In this paper we explain four viewpoints on the local tropicalization of formal subgerms of toric germs, which is a local analog of the global tropicalization of subvarieties of algebraic tori. We start by illustrating some of those viewpoints for plane curve singularities, then we pass to arbitrary dimensions. We conclude by describing several variants and extensions of the notion of local tropicalization presented in this paper.

Date: 2026
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DOI: 10.1007/978-3-031-99571-2_3

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