Author:
Coughlan Stephen,Ducat Tom
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.
Subject
Algebra and Number Theory
Reference33 articles.
1. Fano 3-folds with divisible anticanonical class
2. Computing certain Fano 3-folds;Brown;Jpn. J. Ind. Appl. Math,2007
3. GRDB Brown, G. and Kasprzyk, A. , The graded ring database. Online access via http://www.grdb.co.uk/.
4. ABR02 Altınok, S. , Brown, G. and Reid, M. , Fano 3-folds, K3 surfaces and graded rings, in Topology and geometry: commemorating SISTAG (National University of Singapore, 2001), Contemporary Mathematics, vol. 314, ed. A. J. Berrick (American Mathematical Society Providence, RI, 2002), 25–53.
5. Mat89 Matsumura, H. , Commutative ring theory, Cambridge Studies in Advanced Mathematics, trans. M. Reid (Cambridge, University Press, Cambridge, 1989).
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