Recent progress on the Donaldson-Thomas theory : wall-crossing and refined invariants / / Yukinobu Toda

• Record Nr.: UNISA996466554803316
• Autore: Toda Yukinobu
• Pubbl/distr/stampa: Singapore : , : Springer, , [2021]; ©2021
• ISBN: 981-16-7838-3
• Descrizione fisica: 1 online resource (110 pages)
• Collana: SpringerBriefs in Mathematical Physics
• Disciplina: 512.55
• Soggetti: Algebra, Homological; Algebra - Study and teaching; Invariants; Llibres electrònics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di contenuto: Intro -- Preface -- Contents -- 1 Donaldson-Thomas Invariants on Calabi-Yau 3-Folds -- 1.1 Moduli Spaces of Semistable Sheaves on Algebraic Varieties -- 1.2 Deformation-Obstruction Theory -- 1.3 Donaldson-Thomas Invariants -- 1.4 DT Invariants via Behrend Functions -- 1.5 Rank One DT Invariants -- 2 Generalized Donaldson-Thomas Invariants -- 2.1 An Idea for Generalized DT Theory -- 2.2 Motivic Hall Algebras -- 2.3 Poisson Algebra Homomorphism -- 2.4 Definition of Generalized DT Invariants -- 2.5 Joyce-Song Pair Invariants -- 3 Donaldson-Thomas Invariants for Quivers with Super-Potentials -- 3.1 Introduction to Quivers with Super-Potentials -- 3.2 Moduli Spaces of Representations of Quivers -- 3.3 DT Invariants for Quivers with Super-Potentials -- 3.4 Non-commutative DT Invariants on Resolved Conifold -- 3.5 Analytic Neighborhood Theorem -- 4 Donaldson-Thomas Invariants for Bridgeland Semistable Objects -- 4.1 Definition of Bridgeland Stability Conditions -- 4.2 The Space of Bridgeland Stability Conditions -- 4.3 Constructions of Bridgeland Stability Conditions -- 4.4 Bogomolov-Gieseker-type Inequality -- 4.5 Moduli Spaces of Bridgeland Semistable Objects -- 4.6 DT-type Invariants for Bridgeland Semistable Objects -- 5 Wall-Crossing ; Formulas of Donaldson-Thomas Invariants -- 5.1 An Idea of Wall-Crossing and Applications -- 5.2 General Principle of Wall-Crossing Formulas -- 5.3 DT/PT Correspondence -- 5.4 Rationality of PT Generating Series -- 5.5 Flop Formula of DT Invariants -- 5.6 Jacobi Property for Elliptic CY 3-Folds -- 5.7 PT Invariants for Local K3 Surfaces -- 5.8 Other Applications -- 6 Cohomological Donaldson-Thomas Invariants -- 6.1 Vanishing Cycle Sheaves -- 6.2 D-critical Loci -- 6.3 Gluing of Vanishing Cycle Sheaves -- 6.4 Cohomological DT Invariants -- 6.5 Dual Obstruction Cone.; 6.6 PBW Theorem for Cohomological DT Theory of Quivers with Super-Potentials -- 7 Gopakumar-Vafa Invariants -- 7.1 GW/PT/GV Correspondence Conjecture -- 7.2 Moduli Spaces of One-Dimensional Stable Sheaves -- 7.3 Gopakumar-Vafa Invariants via Vanishing Cycles -- 7.4 PT/GV Correspondence for Local Surfaces -- 8 Some Future Directions -- 8.1 Categorical Donaldson-Thomas Invariants -- 8.2 Donaldson-Thomas Invariants on Calabi-Yau 4-Folds -- 8.3 Cohomological/categorical Hall Algebras -- Appendix References -- -- Index.