Geodesic
Cluster Fan of z-Vectors and Toric Degenerations
Séminaire lotharingien de combinatoire, 80B (2018) 
Gleb Koshevoy. Cluster Fan of z-Vectors and Toric Degenerations. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a95/
@article{SLC_2018_80B_a95,
     author = {Gleb Koshevoy},
     title = {Cluster {Fan} of {z-Vectors} and {Toric} {Degenerations}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2018},
     volume = {80B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a95/}
}
TY  - JOUR
AU  - Gleb Koshevoy
TI  - Cluster Fan of z-Vectors and Toric Degenerations
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a95/
ID  - SLC_2018_80B_a95
ER  - 
%0 Journal Article
%A Gleb Koshevoy
%T Cluster Fan of z-Vectors and Toric Degenerations
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a95/
%F SLC_2018_80B_a95

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

For a cluster algebra, we introduce and study a notion of z-vectors. We prove that z-vectors determine cluster variables. We associate to a cluster seed a simplicial cone being span by z-vectors of the cluster variables of this seed. These cones form a fan, a polyhedral complex, such that the dual graph of this complex is the Fomin-Zelevinsky exchange graph of the cluster algebra.