TY - BOOK

T1 - Faithful tropicalisation and torus actions

AU - Draisma, J.

AU - Postinghel, E.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

M3 - Report

T3 - arXiv

BT - Faithful tropicalisation and torus actions

PB - s.n.

ER -