Birational geometry of cluster algebras
Algebraic Geometry
2014-04-16 v2
Abstract
We give a geometric interpretation of cluster varieties in terms of blowups of toric varieties. This enables us to provide, among other results, an elementary geometric proof of the Laurent phenomenon for cluster algebras (of geometric type), extend Speyer's example of an upper cluster algebra which is not finitely generated, and show that the Fock-Goncharov dual basis conjecture is usually false.
Keywords
Cite
@article{arxiv.1309.2573,
title = {Birational geometry of cluster algebras},
author = {Mark Gross and Paul Hacking and Sean Keel},
journal= {arXiv preprint arXiv:1309.2573},
year = {2014}
}
Comments
50 pages, to appear in Algebraic Geometry