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Cluster tilting for one-dimensional hypersurface singularities
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| Venue: | Adv. Math |
| Citations: | 37 - 16 self |
BibTeX
@ARTICLE{Burban_clustertilting,
author = {Igor Burban and Osamu Iyama and Bernhard Keller and Idun Reiten},
title = {Cluster tilting for one-dimensional hypersurface singularities},
journal = {Adv. Math},
year = {},
pages = {2443--2484}
}
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Abstract
Abstract. In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of cluster tilting objects and their complete description by homological methods, using higher almost split sequences and results from birational geometry. We obtain a large class of 2-CY tilted algebras which are finite dimensional symmetric and satisfy τ 2 = id. In particular, we compute 2-CY tilted algebras for simple and minimally elliptic curve singuralities.
