First Steps in Tropical Intersection Theory

Details First Steps in Tropical Intersection Theory First Steps in Tropical Intersection Theory

2007-09-24

arxiv.org/abs/0709.3705v3

Mathematics

Algebraic Geometry

37 pages, 10 Postscript figures, version 3 coincides with the version to appear in Mathematische Zeitschrift

Scientific paper

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.

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