# 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} }

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

Create an AI-powered research feed to stay up to date with new papers like this posted to ArXiv

#### References

##### Publications referenced by this paper.

SHOWING 1-3 OF 3 REFERENCES

## Discrete Integrable Systems: Qrt Maps and Elliptic Surfaces

VIEW 10 EXCERPTS

HIGHLY INFLUENTIAL

## Difference Scheme of Soliton Equations

VIEW 1 EXCERPT