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Manuscripta Mathematica

, Volume 149, Issue 3–4, pp 315–338 | Cite as

Faithful tropicalisation and torus actions

  • Jan DraismaEmail author
  • Elisa Postinghel
Open Access
Article

Abstract

For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a result due to Cueto, Häbich, and Werner), matrix varieties defined by the vanishing of 3 × 3-minors, and for the hypersurface defined by Cayley’s hyperdeterminant.

Mathematics Subject Classification

14T05 14M15 14M12 14G22 52B40 

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Copyright information

© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands
  2. 2.Vrije UniversiteitAmsterdamThe Netherlands
  3. 3.Centrum voor Wiskunde en InformaticaAmsterdamThe Netherlands
  4. 4.Department of MathematicsKatholieke Universiteit LeuvenLeuvenBelgium

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