6 papers
Categorical absorptions of cone singularities
Martin Kalck, Nebojsa Pavic, with a joint appendix by Yujiro Kawamata +1
We study Kuznetsov-Shinder's categorical absorption for certain cone singularities, generalizing their results for nodal singularities. In particular, we give explicit descriptions…
Magnitude of module categories
Erlend D. Børve, Daniel Horiatakis, Martin Kalck
We define an invariant of the module category of a representation-finite algebra by the magnitude of its Auslander algebra. This invariant will be called the magnitude of the modul…
Length of triangulated categories
Yuki Hirano, Martin Kalck, Genki Ouchi
We introduce the notion of composition series of triangulated categories, which generalizes full exceptional sequences. The lengths of composition series yield invariants for trian…
Relative singularity categories III: Cluster resolutions
Martin Kalck, Dong Yang
We build foundations of an approach to study canonical forms of -Calabi--Yau triangulated categories with cluster-tilting objects, using dg algebras and relative singularity cat…
Dimension formulas for period spaces via motives and species
Annette Huber, Martin Kalck
We apply the structure theory of finite dimensional algebras in order to deduce dimension formulas for spaces of period numbers, i.e., complex numbers defined by integrals of algeb…
Cluster categories for completed infinity-gons I: Categorifying triangulations
Ä°lke Ãanakçı, Martin Kalck, Matthew Pressland
Paquette and Yıldırım recently introduced triangulated categories of arcs in completed infinity-gons, which are discs with an infinite closed set of marked points on their bound…