Faithful tropicalisation and torus actions

Jan Draisma; Elisa Postinghel

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arXiv · 1404.4715

Faithful tropicalisation and torus actions

Jan Draisma·Elisa Postinghel

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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, H\"abich, and Werner), matrix varieties defined by the vanishing of 3 times 3 minors, and for the hypersurface defined by Cayley's hyperdeterminant.

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Jan Draisma, Elisa Postinghel. 2014-04-18. Faithful tropicalisation and torus actions. https://arxiv.org/abs/1404.4715

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