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Record Nr. |
UNINA9910788618203321 |
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Autore |
Joyce Dominic D. |
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Titolo |
A theory of generalized Donaldson-Thomas invariants / / Dominic Joyce, Yinan Song |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , 2012 |
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©2012 |
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ISBN |
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Descrizione fisica |
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1 online resource (199 p.) |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 217, Number 1020 |
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Disciplina |
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Soggetti |
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Donaldson-Thomas invariants |
Calabi-Yau manifolds |
Sheaf theory |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"May 2012, Volume 217, Number 1020 (second of 4 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Chapter 1. Introduction -- 1.1. Brief sketch of background -- 1.2. Behrend functions of schemes and stacks, from chapter 4 -- 1.3. Summary of the main results in chapter 5 -- 1.4. Examples and applications in chapter 6 -- 1.5. Extension to quivers with superpotentials in chapter 7 -- 1.6. Relation to the work of Kontsevich and Soibelman [63] -- Chapter 2. Constructible functions and stack functions -- 2.1. Artin stacks and (locally) constructible functions -- 2.2. Stack functions -- 2.3. Operators and projections -- 2.4. Stack function spaces -- Chapter 3. Background material from [51-54] -- 3.1. Ringel-Hall algebras of an abelian category -- 3.2. (Weak) stability conditions on -- 3.3. Changing stability conditions and algebra identities -- 3.4. Calabi-Yau 3-folds and Lie algebra morphisms -- 3.5. Invariants and transformation laws -- Chapter 4. Behrend functions and Donaldson-Thomas theory -- 4.1. The definition of Behrend functions -- 4.2. Milnor fibres and vanishing cycles -- 4.3. Donaldson-Thomas invariants of Calabi-Yau 3-folds. -- 4.4. Behrend functions and almost closed 1-forms -- 4.5. Characterizing for Calabi-Yau 3-folds -- Chapter 5. Statements of main results -- 5.1. Local description of the moduli of coherent sheaves -- 5.2. Identities on Behrend functions of moduli stacks -- 5.3. A Lie algebra morphism |
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and generalized Donaldson-Thomas invariants -- 5.4. Invariants counting stable pairs, and deformation-invariance -- Chapter 6. Examples, applications, and generalizations. -- 6.1. Computing and in examples 6.2. Integrality properties -- 6.3. Counting dimension zero sheaves -- 6.4. Counting dimension one sheaves -- 6.5. Why it all has to be so complicated: an example -- 6.6. Stability and invariants -- 6.7. Extension to noncompact Calabi-Yau 3-folds -- 6.8. Configuration operations and extended Donaldson-Thomas invariants -- Chapter 7. Donaldson-Thomas theory for quivers with superpotentials -- 7.1. Introduction to quivers -- 7.2. Quivers with superpotentials, and 3-Calabi-Yau categories. -- 7.3. Behrend function identities, Lie algebra morphisms, and Donaldson-Thomas type invariants 7.4. Pair invariants for quivers -- 7.5. Computing in examples -- 7.6. Integrality of for generic -- Chapter 8. The proof of Theorem 5.3 -- Chapter 9. The proofs of Theorems 5.4 and 5.5 -- 9.1. Holomorphic structures on a complex vector bundle -- 9.2. Moduli spaces of analytic vector bundles on -- 9.3. Constructing a good local atlas for near -- 9.4. Moduli spaces of algebraic vector bundles on. -- 9.5. Identifying versal families of holomorphic structures and algebraic vector bundles. |
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