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Search: All articles in the CJM digital archive with keyword tropical geometry

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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 equivalenceCategory:14T05

2. CJM 2014 (vol 67 pp. 527)

Brugallé, Erwan; Shaw, Kristin
 Obstructions to Approximating Tropical Curves in Surfaces Via Intersection Theory We provide some new local obstructions to approximating tropical curves in smooth tropical surfaces. These obstructions are based on a relation between tropical and complex intersection theories which is also established here. We give two applications of the methods developed in this paper. First we classify all locally irreducible approximable 3-valent fan tropical curves in a fan tropical plane. Secondly, we prove that a generic non-singular tropical surface in tropical projective 3-space contains finitely many approximable tropical lines if it is of degree 3, and contains no approximable tropical lines if it is of degree 4 or more. Keywords:tropical geometry, amoebas, approximation of tropical varieties, intersection theoryCategories:14T05, 14M25

3. CJM 2012 (vol 65 pp. 120)

Francois, Georges; Hampe, Simon
 Universal Families of Rational Tropical Curves We introduce the notion of families of $n$-marked smooth rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical varieties into the moduli space of $n$-marked abstract rational tropical curves $\mathcal{M}_{n}$. Keywords:tropical geometry, universal family, rational curves, moduli spaceCategories:14T05, 14D22
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