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Relative singularity categories III: Cluster resolutions

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arxiv 2006.09733 v2 pith:AXRD53FL submitted 2020-06-17 math.RT math.ACmath.AGmath.CT

Martin Kalck , Dong Yang This is my paper · ORCID
classification math.RTmath.ACmath.AGmath.CT
keywords categoriessingularityclusterrelativealgebrasapproachbuildcalabi--yau
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abstract

We build foundations of an approach to study canonical forms of $2$-Calabi--Yau triangulated categories with cluster-tilting objects, using dg algebras and relative singularity categories. This is motivated by cluster theory, singularity categories, Wemyss's Homological Minimal Model Program and the relations between these topics.

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  1. From objects finitely presented by a rigid object in a triangulated category to 2-term complexes

    math.RT 2025-09 accept novelty 6.0 of 10

    For a rigid object M, the presentation functor P from pr(M) to 2-term complexes over End(M) is full, dense, detects extriangles, and induces a mutation-commuting bijection between basic relative cluster-tilting object...

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