Geodesic
Stable intersections of tropical varieties
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 101-128.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We give several characterizations of stable intersections of tropical cycles and establish their fundamental properties. We prove that the stable intersection of two tropical varieties is the tropicalization of the intersection of the classical varieties after a generic rescaling. A proof of Bernstein's theorem follows from this. We prove that the tropical intersection ring of tropical cycle fans is isomorphic to McMullen's polytope algebra. It follows that every tropical cycle fan is a linear combination of pure powers of tropical hypersurfaces, which are always realizable. We prove that every stable intersection of constant coefficient tropical varieties defined by prime ideals is connected through codimension one. We also give an example of a realizable tropical variety that is connected through codimension one but whose stable intersection with a hyperplane is not.
Classification : 14T05, 14C17
Keywords: tropical geometry, intersection theory, polytope algebra 
@article{JAC_2016__43_1_a6,
     author = {Jensen, Anders and Yu, Josephine},
     title = {Stable intersections of tropical varieties},
     journal = {Journal of Algebraic Combinatorics},
     pages = {101--128},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a6/}
}
TY  - JOUR
AU  - Jensen, Anders
AU  - Yu, Josephine
TI  - Stable intersections of tropical varieties
JO  - Journal of Algebraic Combinatorics
PY  - 2016
SP  - 101
EP  - 128
VL  - 43
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a6/
LA  - en
ID  - JAC_2016__43_1_a6
ER  - 
%0 Journal Article
%A Jensen, Anders
%A Yu, Josephine
%T Stable intersections of tropical varieties
%J Journal of Algebraic Combinatorics
%D 2016
%P 101-128
%V 43
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a6/
%G en
%F JAC_2016__43_1_a6
Jensen, Anders; Yu, Josephine. Stable intersections of tropical varieties. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 101-128. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a6/