Cluster tilting for one-dimensional hypersurface singularities

This is a joint work with I. Burban, B. Keller and I. Reiten.

We consider the category of maximal Cohen-Macaulay modules over one-dimensional

hypersurface singularities. This category enjoys 2-Calabi-Yau property. We shall classify

cluster tilting object in this category by applying general results on higher Auslander

algebras and (cluster) tilting mutation theory.

Osamu Iyama