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arXiv · 1811.10926

Constructing Fano 3-folds from cluster varieties of rank 2

Stephen Coughlan·Tom Ducat
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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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Stephen Coughlan, Tom Ducat. 2018-11-27. Constructing Fano 3-folds from cluster varieties of rank 2. https://doi.org/10.1112/s0010437x20007368

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