Torus actions and faithful tropicalisations

Algebra Seminar
Friday, April 11, 2014 - 11:05am for 1 hour (actually 50 minutes)
Skiles 005
Jan Draisma – TU Eindhoven –
Josephine Yu
Given a closed subvariety X of affine space A^n, there is a surjective map from the analytification of X to its tropicalisation. The natural question arises, whether this map has a continuous section. Recent work by Baker, Payne, and Rabinoff treats the case of curves, and even more recent work by Cueto, Haebich, and Werner treats Grassmannians of 2-spaces. I will sketch how one can often construct such sections when X is obtained from a linear space smeared around by a coordinate torus action. In particular, this gives a new, more geometric proof for the Grassmannian of 2-spaces; and it also applies to some determinantal varieties. (Joint work with Elisa Postinghel)