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.
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JD is supported by a Vidi grant from the Netherlands Organisation for Scientific Research (NWO).
EP is supported by the Research Foundation-Flanders (FWO).
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Draisma, J., Postinghel, E. Faithful tropicalisation and torus actions. manuscripta math. 149, 315–338 (2016). https://doi.org/10.1007/s00229-015-0781-3
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DOI: https://doi.org/10.1007/s00229-015-0781-3