2018/11/30 by Stephen Coughlan, Tom Ducat · 14 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Artificial intelligence #Class (philosophy) #Cluster (spacecraft) #Cluster algebra #Codimension #Combinatorics #Computer science #Construct (python library) #Fano plane #Geometry #Mathematics #Physics #Pure mathematics #Quantum #Rank (graph theory) #Symmetry (geometry) #math.AG
paper · pdf · doi:10.1112/s0010437x20007368
published in Compositio Mathematica 156(9), 1873-1914 (Cambridge University Press) · Minor changes following referee report, to appear in Compositio Mathematica, 44 pages, 4 figures
arxiv created 2019/11/01 · openalex publication_date 2020/09/01 · arxiv updated 2020/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.