Abstract. In this article we study Cohen-Macaulay modules over one-dimensional hypersurface singularities and the relationship with 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 method 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 satisfies τ 2 = id. In particular, we compute 2-CY tilted algebras for simple/minimally elliptic curve singuralities.

Abstract. In this paper we give a survey about the classification of vector bundles and torsion free sheaves on degenerations of elliptic curves. Coherent sheaves on singular curves of arithmetic genus one can be studied using the technique of matrix problems or via Fourier-Mukai transforms, both methods are discussed here. Moreover, we include new proofs of some classical results about vector bundles on elliptic curves.

Abstract not found

Abstract not found

1. An easy example: vector bundles on P1 4 2. A simple example: projective configurations of type A 4 3. Elliptic curves are vector bundle tame 7