Corpus ID: 119152315

Constructing Fano 3-folds from cluster varieties of rank 2

  title={Constructing Fano 3-folds from cluster varieties of rank 2},
  author={Stephen Coughlan and Tom Ducat},
  journal={arXiv: Algebraic Geometry},
  • Stephen Coughlan, Tom Ducat
  • Published 2018
  • Mathematics
  • arXiv: Algebraic Geometry
  • Cluster algebras give rise to a class of Gorenstein rings which enjoy a large amount of symmetry. Concentrating on the rank 2 cases, we show how cluster varieties can be used to construct many interesting projective algebraic varieties. Our main application is then to construct hundreds of families of Fano 3-folds in codimensions 4 and 5. In particular, for Fano 3-folds in codimension 4 we construct at least one family for 187 of the 206 possible Hilbert polynomials contained in the Graded Ring… CONTINUE READING

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    Birationally superrigid Fano 3-folds of codimension 4


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