Michael Barot, Dirk Kussin, Helmut Lenzing
Published 2008-01-29, updated 2009-01-29Version 3
We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. As an application we determine the automorphism group of the cluster category and show that the cluster-tilting objects form a cluster structure in the sense of Buan-Iyama-Reiten-Scott. The tilting graph of the sheaf category always coincides with the tilting or exchange graph of the cluster category. We show that this graph is connected if the Euler characteristic of X is non-negative, or equivalently, if A is of tame (domestic or tubular) representation type.
Comments: 16 pages. A few minor changes, one reference added. To appear in Trans. Amer. Math. Soc
The Grothendieck group of a cluster category
A geometric description of $m$-cluster categories
Geometric characterizations of the representation type of hereditary algebras and of canonical algebras
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