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arXiv · 0704.1249

Cluster tilting for one-dimensional hypersurface singularities

Igor Burban·Osamu Iyama·Bernhard Keller·Idun Reiten
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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 singularities.

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BibTeXRIS

Igor Burban, Osamu Iyama, Bernhard Keller, Idun Reiten. 2007-10-01. Cluster tilting for one-dimensional hypersurface singularities. https://arxiv.org/abs/0704.1249

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