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Asymptotic behaviour of tame harmonic bundles and an application to pure twister D-modules. Part 2 /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Mochizuki, Takuro, 1972-
Autor Corporativo: American Mathematical Society
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence, R.I. : American Mathematical Society, 2007.
Colección:Memoirs of the American Mathematical Society ; no. 870.
Temas:
Acceso en línea:Texto completo
Tabla de Contenidos:
  • ""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 algebra2.8. 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 bundles3.6. 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 divisorsChapter 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
  • ""7.5. The case where λ is generic""""7.6. Family of multi-valued sections""; ""7.7. Asymptotic orthogonality""; ""7.8. Maximum principle for the distance of the harmonic metrics""; ""Chapter 8. Harmonic Bundles on a Product of Punctured Discs""; ""8.1. Preliminary""; ""8.2. Simpson's Main estimate in the higher dimensional case""; ""8.3. Prolongation in the case that λ is generic""; ""8.4. Extension of holomorphic sections on a hyper plane""; ""8.5. Preliminary prolongation of ελ (Special case)""; ""8.6. Prolongation of ελ and the compatibility of the parabolic filtrations""