Faithful tropicalisation and torus actions

J. Draisma, E. Postinghel

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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, H\"abich, and Werner), matrix varieties defined by the vanishing of maximal minors or of 3 times 3 minors, and for the hypersurface defined by Cayley's hyperdeterminant.
Original languageEnglish
Number of pages20
Publication statusPublished - 2014

Publication series

Volume1404.4715 [math.AG]


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