Faithful tropicalisation and torus actions

Draisma, Jan; Postinghel, Elisa (2016). Faithful tropicalisation and torus actions. Manuscripta mathematica, 149(3-4), pp. 315-338. Springer 10.1007/s00229-015-0781-3

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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, Häbich, and Werner), matrix varieties defined by the vanishing of 3 X 3 minors, and for the hypersurface defined by Cayley's hyperdeterminant.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Draisma, Jan

Subjects:

500 Science > 510 Mathematics

ISSN:

0025-2611

Publisher:

Springer

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

31 Jul 2017 15:06

Last Modified:

11 Sep 2017 17:35

Publisher DOI:

10.1007/s00229-015-0781-3

ArXiv ID:

1404.4715v3

BORIS DOI:

10.7892/boris.99759

URI:

https://boris.unibe.ch/id/eprint/99759

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