2020/03/19 by Gil, J. I. Burgos, Gubler, W., Jell, P. +1 · 1 citation
#32U05 #32U40 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT) #Primary 14L32 #Secondary 14T05
paper · doi:10.48550/arxiv.2003.08644
Given a smooth complex toric variety we will compare real Lagerberg forms and currents on its tropicalization with invariant complex forms and currents on the toric variety. Our main result is a correspondence theorem which identifies the cone of invariant closed positive currents on the complex toric variety with closed positive currents on the tropicalization. In a subsequent paper, this correspondence will be used to develop a Bedford-Taylor theory of plurisubharmonic functions on the tropicalization.