Results 1  10
of
12
Cluster tilting for onedimensional hypersurface singularities
 Adv. Math
"... Abstract. In this article we study CohenMacaulay modules over onedimensional 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 d ..."
Abstract

Cited by 37 (15 self)
 Add to MetaCart
Abstract. In this article we study CohenMacaulay modules over onedimensional 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 2CY tilted algebras which are finite dimensional symmetric and satisfies τ 2 = id. In particular, we compute 2CY tilted algebras for simple/minimally elliptic curve singuralities.
Vector bundles and torsion free sheaves on degenerations of elliptic curves. Global Aspects of Complex Analisys
, 2006
"... 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 FourierMukai transforms, both me ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
(Show Context)
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 FourierMukai transforms, both methods are discussed here. Moreover, we include new proofs of some classical results about vector bundles on elliptic curves.
REPRESENTATION THEORY FOR LOGCANONICAL SURFACE SINGULARITIES
"... Abstract. We consider the representation theory for a class of logcanonical surface singularities in the sense of reflexive (or equivalently maximal CohenMacaulay) modules and in the sense of finite dimensional representations of the local fundamental group. A detailed classification and enumerati ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
Abstract. We consider the representation theory for a class of logcanonical surface singularities in the sense of reflexive (or equivalently maximal CohenMacaulay) modules and in the sense of finite dimensional representations of the local fundamental group. A detailed classification and enumeration of the indecomposable reflexive modules is given, and we prove that any reflexive module admits an integrable connection and hence is induced from a finite dimensional representation of the local fundamental group. 1.
COHEN–MACAULAY MODULES OVER SOME NON–REDUCED CURVE SINGULARITIES
"... Abstract. In this article, we study Cohen–Macaulay modules over non–reduced curve singularities. We prove that the rings kJx, y, zK/(xy, yq−z2) have tame Cohen–Macaulay representation type. For the singularity kJx, y, zK/(xy, z2) we give an explicit description of all indecomposable Cohen–Macaulay m ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. In this article, we study Cohen–Macaulay modules over non–reduced curve singularities. We prove that the rings kJx, y, zK/(xy, yq−z2) have tame Cohen–Macaulay representation type. For the singularity kJx, y, zK/(xy, z2) we give an explicit description of all indecomposable Cohen–Macaulay modules and apply the obtained classification to construct explicit families of indecomposable matrix factorizations of x2y2 ∈ kJx, yK.