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 -