Canonical bases for cluster algebras

  title={Canonical bases for cluster algebras},
  author={Mark Gross and Paul Hacking and S. Keel and Maxim Kontsevich},
  journal={Journal of the American Mathematical Society},
In [GHK11], Conjecture 0.6, the first three authors conjectured that the ring of regular functions on a natural class of affine log Calabi-Yau varieties (those with maximal boundary) has a canonical vector space basis parameterized by the integral tropical points of the mirror. Further, the structure constants for the multiplication rule in this basis should be given by counting broken lines (certain combinatorial objects, morally the tropicalisations of holomorphic discs). Here we prove the… Expand
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