Corpus ID: 119606074

Birational maps conjugate to the rank 2 cluster mutations of affine types and their geometry

@inproceedings{Nobe2018BirationalMC,
  title={Birational maps conjugate to the rank 2 cluster mutations of affine types and their geometry},
  author={Atsushi Nobe},
  year={2018}
}
  • Atsushi Nobe
  • Published 2018
  • Mathematics, Physics
  • Mutations of the cluster variables generating the cluster algebra of type $A^{(2)}_2$ reduce to a two-dimensional discrete integrable system given by a quartic birational map. The invariant curve of the map is a singular quartic curve, and its resolution of the singularity induces a discrete integrable system on a conic governed by a cubic birational map conjugate to the cluster mutations of type $A^{(2)}_2$. Moreover, it is shown that the conic is also the invariant curve of the quadratic… CONTINUE READING

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