On Rational Equivalence in Tropical Geometry
Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 241-257
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This article discusses the concept of rational equivalence in tropical geometry (and replaces an older, imperfect version). We give the basic definitions in the context of tropical varieties without boundary points and prove some basic properties. We then compute the “bounded” Chow groups of ${{\mathbf{R}}^{n}}$ by showing that they are isomorphic to the group of fan cycles. The main step in the proof is of independent interest. We show that every tropical cycle in ${{\mathbf{R}}^{n}}$ is a sum of (translated) fan cycles. This also proves that the intersection ring of tropical cycles is generated in codimension 1 (by hypersurfaces).
Allermann, Lars; Hampe, Simon; Rau, Johannes. On Rational Equivalence in Tropical Geometry. Canadian journal of mathematics, Tome 68 (2016) no. 2, pp. 241-257. doi: 10.4153/CJM-2015-036-0
@article{10_4153_CJM_2015_036_0,
author = {Allermann, Lars and Hampe, Simon and Rau, Johannes},
title = {On {Rational} {Equivalence} in {Tropical} {Geometry}},
journal = {Canadian journal of mathematics},
pages = {241--257},
year = {2016},
volume = {68},
number = {2},
doi = {10.4153/CJM-2015-036-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-036-0/}
}
TY - JOUR AU - Allermann, Lars AU - Hampe, Simon AU - Rau, Johannes TI - On Rational Equivalence in Tropical Geometry JO - Canadian journal of mathematics PY - 2016 SP - 241 EP - 257 VL - 68 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-036-0/ DO - 10.4153/CJM-2015-036-0 ID - 10_4153_CJM_2015_036_0 ER -
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