A New Triangulated Category for Rational Surface Singularities

2009/05/25 by Osamu Iyama, Iyama, Osamu, Michael Wemyss +1 · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0905.3940

openalex publication_date 2009/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short paper we introduce a new triangulated category for rational surface singularities which in the non-Gorenstein case acts as a substitute for the stable category of matrix factorizations. The category is formed as a Frobenius quotient of the category of special CM modules, and we classify the relatively projective-injective objects and thus describe the AR quiver of the quotient. Connections to the corresponding reconstruction algebras are also discussed.

Cited by

• Replicated algebras derived equivalent to higher Auslander algebras of type A
• Coxeter matrices and homological quadratic forms of \boldsymboln-hereditary algebras

Related

• Triangulated categories of Gorenstein cyclic quotient singularities
• Relative singularity category of a non-commutative resolution of\n singularities
• Categorical aspects of the Kollár--Shepherd-Barron correspondence
• Reduction of triangulated categories and Maximal Modification Algebras for cA_n singularities
• Derived categories of singular surfaces