First steps in tropical intersection theory

Abstract

We establish first parts of a tropical intersection theory. Namely, we define cycles, Cartier divisors and intersection products between these two (without passing to rational equivalence) and discuss push-forward and pull-back. We do this first for fans in $${\mathbb{R}^{n}}$$ and then for “abstract” cycles that are fans locally. With regard to applications in enumerative geometry, we finally have a look at rational equivalence and intersection products of cycles and cycle classes in $${\mathbb{R}^{n}}$$ .