# Tropical intersection theory from toric varieties

@article{Katz2009TropicalIT,
title={Tropical intersection theory from toric varieties},
author={Eric Katz},
journal={Collectanea Mathematica},
year={2009},
volume={63},
pages={29-44}
}
• Eric Katz
• Published 15 July 2009
• Mathematics
• Collectanea Mathematica
We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on compact toric varieties. These objects fit into the framework of tropical intersection theory developed by Allermann and Rau. Standard facts about intersection theory on toric varieties are applied to show that the definitions of tropical intersection product on tropical…
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In these notes we survey the tropical intersection theory on R^n by deriving the properties for tropical cycles from the corresponding properties in Chow cohomology. For this we review the stable
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• 2013
We show that points in the intersection of the tropicaliza- tions of subvarieties of a torus lift to algebraic intersection points with expected multiplicities, provided that the tropicalizations
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