First Steps in Tropical Intersection Theory
Algebraic Geometry
2012-11-07 v3 Combinatorics
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 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 R^n.
Cite
@article{arxiv.0709.3705,
title = {First Steps in Tropical Intersection Theory},
author = {Lars Allermann and Johannes Rau},
journal= {arXiv preprint arXiv:0709.3705},
year = {2012}
}
Comments
37 pages, 10 Postscript figures, version 3 coincides with the version to appear in Mathematische Zeitschrift