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Polygons of Finite Mutation Type

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Interactions with Lattice Polytopes (ILP 2017)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 386))

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Abstract

We classify Fano polygons with finite mutation class. This classification exploits a correspondence between Fano polygons and cluster algebras, refining the notion of singularity content due to Akhtar and Kasprzyk. We also introduce examples of cluster algebras associated to Fano polytopes in dimensions greater than two.

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Acknowledgements

We thank Alexander Kasprzyk for his insights on polytope mutation, and our many conversations about quivers. The author is supported by a Fellowship by Examination at Magdalen College, Oxford. This work was undertaken while the author was a graduate student at Imperial College London.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Woodstock Road, Oxford, OX2 6GG, UK

    Thomas Prince

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  1. Thomas Prince
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Correspondence to Thomas Prince .

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Editors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Alexander M. Kasprzyk

  2. Fakultät für Mathematik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Benjamin Nill

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Prince, T. (2022). Polygons of Finite Mutation Type. In: Kasprzyk, A.M., Nill, B. (eds) Interactions with Lattice Polytopes. ILP 2017. Springer Proceedings in Mathematics & Statistics, vol 386. Springer, Cham. https://doi.org/10.1007/978-3-030-98327-7_15

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