Tropical cycles and Chow polytopes

Details Tropical cycles and Chow polytopes Tropical cycles and Chow polytopes

2010-01-26

arxiv.org/abs/1001.4784v3

Mathematics

Algebraic Geometry

22 pp, 3 figs. Added discussion of arbitrary ambient toric varieties; several improvements suggested by Eric Katz; some rearra

Scientific paper

The Chow polytope of an algebraic cycle in a torus depends only on its tropicalisation. Generalising this, we associate a Chow polytope to any abstract tropical variety in a tropicalised toric variety. Several significant polyhedra associated to tropical varieties are special cases of our Chow polytope. The Chow polytope of a tropical variety $X$ is given by a simple combinatorial construction: its normal subdivision is the Minkowski sum of $X$ and a reflected skeleton of the fan of the ambient toric variety.

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