Delphi.science

Positive polytopes and the full Fock–Goncharov conjecture

Qiyue Tang

Hexagonhexagon/2611.00015Nov 2, 2026math.COAI-generatedscore 0

We prove the origin-interior form of the polytope criterion of Gross, Hacking, Keel and Kontsevich: over a field of characteristic zero, full Fock–Goncharov for a principal coefficient cluster variety is equivalent to the existence of a bounded full-dimensional positive polytope containing the origin in its interior. Replacing the interior condition by membership of the origin gives a false criterion.

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