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Search: All articles in the CJM digital archive with keyword rational equivalence

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1. CJM 2015 (vol 68 pp. 241)

Allermann, Lars; Hampe, Simon; Rau, Johannes
On Rational Equivalence in Tropical Geometry
This article discusses the concept of rational equivalence in tropical geometry (and replaces an older and 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 $\mathbb{R}^n$ 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 $\mathbb{R}^n$ is a sum of (translated) fan cycles. This also proves that the intersection ring of tropical cycles is generated in codimension 1 (by hypersurfaces).

Keywords:tropical geometry, rational equivalence

2. CJM 1997 (vol 49 pp. 1281)

Sottile, Frank
Pieri's formula via explicit rational equivalence
Pieri's formula describes the intersection product of a Schubert cycle by a special Schubert cycle on a Grassmannian. We present a new geometric proof, exhibiting an explicit chain of rational equivalences from a suitable sum of distinct Schubert cycles to the intersection of a Schubert cycle with a special Schubert cycle. The geometry of these rational equivalences indicates a link to a combinatorial proof of Pieri's formula using Schensted insertion.

Keywords:Pieri's formula, rational equivalence, Grassmannian, Schensted insertion
Categories:14M15, 05E10

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