Theta bases are atomic

Travis Mandel

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

Fock and Goncharov conjectured that the indecomposable universally positive (i.e. atomic) elements of a cluster algebra should form a basis for the algebra. This was shown to be false by Lee, Li and Zelevinsky. However, we find that the theta bases of Gross, Hacking, Keel and Kontsevich do satisfy this conjecture for a slightly modified definition of universal positivity in which one replaces the positive atlas consisting of the clusters by an enlargement we call the scattering atlas. In particular, this uniquely characterizes the theta functions.
Original languageEnglish
Pages (from-to)1217-1219
JournalCompositio Mathematica
Volume153
Issue number6
Early online date26 Apr 2017
DOIs
Publication statusPublished - 1 Jun 2017

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