Asymptotic behaviour of tame harmonic bundles and an application to pure twistor D-modules . Part 1 / / Takuro Mochizuki

• Record Nr.: UNINA9910812437703321
• Autore: Mochizuki Takuro <1972->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , [2007]; ©2007
• ISBN: 1-4704-0473-7
• Descrizione fisica: 1 online resource (344 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; number 869
• Disciplina: 514.74
• Soggetti: Hodge theory; D-modules; Vector bundles; Harmonic maps
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: ""Contents""; ""Acknowledgement""; ""Chapter 1. Introduction""; ""1.1. Simpson's Meta-Theorem""; ""1.2. The purposes in this paper""; ""1.3. On the purpose (1)""; ""1.4. On the purpose (2)""; ""1.5. Some Remark""; ""1.6. The outline of the paper""; ""Part 1. Preliminary""; ""Chapter 2. Preliminary""; ""2.1. Notation""; ""2.2. Prolongation by an increasing order""; ""2.3. Preliminary for Î?c-equivariant bundle""; ""2.4. Some elementary preliminary for convexity""; ""2.5. Some lemmas for functions on a disc""; ""2.6. An elementary remark on some distributions""; ""2.7. Preliminary from elementary linear algebra""""2.8. Preliminary from complex differential geometry""; ""2.9. Preliminary from functional analysis""; ""2.10. An estimate of the norms of Higgs field and the conjugate""; ""2.11. Convergency of the sequence of harmonic bundles""; ""2.12. Higgs field and twisted map""; ""Chapter 3. Preliminary for Mixed Twistor Structure""; ""3.1. P[sup(1)]-holomorphic vector bundle over X x P[sup(1)]""; ""3.2. Equivariant P[sup(1)]-holomorphic bundle over X x P[sup(1)]""; ""3.3. Tate objects and O(p,q)""; ""3.4. Equivalence of some categories""; ""3.5. Variation of P[sup(1)]-holomorphic bundles""""3.6. The twistor nilpotent orbit""; ""3.7. Split polarized mixed twistor structure and the nilpotent orbit""; ""3.8. The induced tuple on the divisor""; ""3.9. Translation of some results due to Kashiwara, Kawai and Saito""; ""3.10. R-triple in dimension 0 and twistor structure""; ""Chapter 4. Preliminary for Filtrations""; ""4.1. Filtrations and decompositions on a vector space""; ""4.2. Filtrations and decompositions on a vector bundle""; ""4.3. Compatibility of the filtrations and nilpotent maps""; ""4.4. Extension of splittings""; ""4.5. Compatibility of the filtrations and nilpotent maps on the divisors""""Chapter 5. Some Lemmas for Generically Splitted Case""; ""5.1. Filtrations""; ""5.2. Compatibility of morphisms and filtrations""; ""Chapter 6. Model Bundles""; ""6.1. Basic example I""; ""6.2. Basic example II""; ""Part 2. Prolongation of Deformed Holomorphic Bundles""; ""Chapter 7. Harmonic Bundles on a Punctured Disc""; ""7.1. Simpson's main estimate""; ""7.2. The KMS-structure of tame harmonic bundles on a punctured disc""; ""7.3. Basic comparison due to Simpson""; ""7.4. Multi-valued flat sections""