Year: 2015
Type: article
Abstract: This article discusses the concept of rational equivalence in tropical geometry (and replaces an older, imperfect version). We give the basic definitions in the context of tropical varieties without boundary points and prove some basic properties. We then compute the “bounded” Chow groups of Rn by showing that they are isomorphic to the group of fan cycles. The main step in the proof is of independent interest. We show that every tropical cycle in Rn is a sum of (translated) fan cycles. This also proves that the intersection ring of tropical cycles is generated in codimension 1 (by hypersurfaces).
Source: Canadian Journal of Mathematics
Authors: Lars Allermann, Simon Hampe, Johannes Rau
Institutions: University of Kaiserslautern, Saarland University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1937430554