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Faithful tropicalisation and torus actions
journal contributionposted on 2016-11-07, 10:43 authored by Jan Draisma, Elisa Postinghel
© 2015, The Author(s).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.
- Mathematical Sciences
Published inManuscripta Mathematica
Pages315 - 338
CitationDRAISMA, J. and POSTINGHEL, E., 2016. Faithful tropicalisation and torus actions. Manuscripta Mathematica, 149(3-4), pp. 315-338.
Publisher© The Authors. Published by Springer.
- VoR (Version of Record)
Publisher statementThis work is made available according to the conditions of the Creative Commons Attribution 4.0 International (CC BY 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/ by/4.0/
NotesThis is an Open Access Article. It is published by Springer under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/