62 citations · 265 across the 23 of their papers we have counts for
24 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…
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…
Obstructions to semiorthogonal decompositions for singular projective varieties II: Representation theory
Martin Kalck, Carlo Klapproth, Nebojsa Pavic
We show that odd-dimensional projective varieties with tilting objects and only ADE-hypersurface singularities are nodal, i.e. they only have -singularities. This is a very sp…
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…
Cluster categories for completed infinity-gons I: Categorifying triangulations
İlke Çanakçı, 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 boundary…
A finite dimensional algebra with a phantom (a corollary of an example by J. Krah)
Martin Kalck
We observe that there exists an associative finite dimensional -algebra of finite global dimension, such that the bounded derived category of finite dimens…
Classifying dg-categories of matrix factorizations
Martin Kalck
We give a complete classification of differential -graded homotopy categories of matrix factorizations of isolated singularities up to quasi-equivalence. This answers a…
A new equivalence between singularity categories of commutative algebras
Martin Kalck
We construct a triangle equivalence between the singularity categories of two isolated cyclic quotient singularities of Krull dimensions two and three, respectively. This is the fi…
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…
Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory
Martin Kalck, Nebojsa Pavic, Evgeny Shinder
We investigate necessary conditions for Gorenstein projective varieties to admit semiorthogonal decompositions introduced by Kawamata, with main emphasis on threefolds with isolate…
Relative singularity categories II: DG models
Martin Kalck, Dong Yang
We study the relationship between singularity categories and relative singularity categories and discuss constructions of differential graded algebras of relative singularity categ…
Ringel duality for certain strongly quasi-hereditary algebras
Martin Kalck, Joseph Karmazyn
We introduce quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The main result is a uniform fo…
A remark on Leclerc's Frobenius categories
Martin Kalck
Leclerc recently studied certain Frobenius categories in connection with cluster algebra structures on coordinate rings of intersections of opposite Schubert cells. We show that th…
Relative Singularity Categories
Martin Kalck
We study the following generalization of singularity categories. Let X be a quasi-projective Gorenstein scheme with isolated singularities and A a non-commutative resolution of sin…
Noncommutative Knörrer type equivalences via noncommutative resolutions of singularities
Martin Kalck, Joseph Karmazyn
We construct Knörrer type equivalences outside of the hypersurface case, namely, between singularity categories of cyclic quotient surface singularities and certain finite dimensio…
Derived categories of graded gentle one-cycle algebras
Martin Kalck, Dong Yang
Let be a graded algebra. It is shown that the derived category of dg modules over (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orb…
Derived categories of quasi-hereditary algebras and their derived composition series
Martin Kalck
We study composition series of derived module categories in the sense of Angeleri Hügel, König & Liu for quasi-hereditary algebras. More precisely, we show that having a compositio…
Spherical subcategories in representation theory
Andreas Hochenegger, Martin Kalck, David Ploog
We introduce a new invariant for triangulated categories: the poset of spherical subcategories ordered by inclusion. This yields several numerical invariants, like the cardinality…
Frobenius categories, Gorenstein algebras and rational surface singularities
Osamu Iyama, Martin Kalck, Michael Wemyss +1
We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga-Gorenstein ring. We then apply this result…
Spherical subcategories in algebraic geometry
Andreas Hochenegger, Martin Kalck, David Ploog
We study objects in triangulated categories which have a two-dimensional graded endomorphism algebra. Given such an object, we show that there is a unique maximal triangulated subc…
Singularity categories of gentle algebras
Martin Kalck
We determine the singularity category of an arbitrary finite dimensional gentle algebra . It is a finite product of -cluster categories of type . Equivalently…
Relative singularity categories I: Auslander resolutions
Martin Kalck, Dong Yang
Let be an isolated Gorenstein singularity with a non-commutative resolution . In this paper, we show that the relative singularity category of …
Relative singularity category of a non-commutative resolution of singularities
Igor Burban, Martin Kalck
In this article we study the triangulated category of singularities associated with a non-commutative resolution of singularities. In particular, we give a complete description of…