Constructing Fano 3-folds from cluster varieties of rank 2
Algebraic Geometry
2020-11-11 v2
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.
Keywords
Cite
@article{arxiv.1811.10926,
title = {Constructing Fano 3-folds from cluster varieties of rank 2},
author = {Stephen Coughlan and Tom Ducat},
journal= {arXiv preprint arXiv:1811.10926},
year = {2020}
}
Comments
Minor changes following referee report, to appear in Compositio Mathematica, 44 pages, 4 figures