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Constructing Fano 3-folds from cluster varieties of rank 2
Published online by Cambridge University Press: 09 November 2020
Abstract
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 Database.
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- Copyright © The Author(s) 2020
Footnotes
Current address: Department of Mathematics, Imperial College, South Kensington Campus, Huxley Building, 180 Queen's Gate, London, SW7 2AZ, UK
To Miles Reid on his 70th birthday.
References
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