Donaldson-Thomas theory and cluster algebras

DOI10.1215/00127094-2142753zbMath1375.14150arXiv1002.4884OpenAlexW2964251143MaRDI QIDQ2376817

Kentaro Nagao

Publication date: 24 June 2013

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.4884

Mathematics Subject Classification ID

Vector bundles on surfaces and higher-dimensional varieties, and their moduli (14J60) Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) (14N35) Cluster algebras (13F60)

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Cites Work

• Unnamed Item
• Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants
• Quiver varieties and cluster algebras
• Cluster characters for cluster categories with infinite-dimensional morphism spaces
• Derived equivalences from mutations of quivers with potential
• An introduction to motivic Hall algebras
• Configurations in abelian categories. II: Ringel-Hall algebras
• Non-commutative Donaldson-Thomas invariants and the conifold
• Donaldson-Thomas type invariants via microlocal geometry
• Quivers with potentials and their representations. I: Mutations.
• The Harder-Narasimhan system in quantum groups and cohomology of quiver moduli
• A holomorphic Casson invariant for Calabi-Yau 3-folds, and bundles on \(K3\) fibrations.
• Configurations in abelian categories. IV: Invariants and changing stability conditions
• Stability conditions on triangulated categories
• Cluster algebras as Hall algebras of quiver representations.
• Cluster algebras I: Foundations
• A theory of generalized Donaldson–Thomas invariants
• Deformed Calabi–Yau completions
• Cluster algebras, quiver representations and triangulated categories
• Hall algebras and curve-counting invariants
• Cluster algebras IV: Coefficients
• Quivers with potentials and their representations II: Applications to cluster algebras
• Gromov–Witten theory and Donaldson–Thomas theory, I
• On tropical dualities in cluster algebras
• Periodicities in cluster algebras and dilogarithm identities