Contents
Acknowledgement xii
Chapter 1. Introduction 1
1.1. Simpson's Meta-Theorem 1
1.2. The purposes in this paper 1
1.3. On the purpose (1) 1
1.4. On the purpose (2) 7
1.5. Some Remark 10
1.6. The outline of the paper 10
Part 1. Preliminary 23
Chapter 2. Preliminary 24
2.1. Notation 24
2.2. Prolongation by an increasing order 26
2.3. Preliminary for /xc-equivariant bundle 28
2.4. Some elementary preliminary for convexity 30
2.5. Some lemmas for functions on a disc 33
2.6. An elementary remark on some distributions 36
2.7. Preliminary from elementary linear algebra 39
2.8. Preliminary from complex differential geometry 41
2.9. Preliminary from functional analysis 52
2.10. An estimate of the norms of Higgs field and the conjugate 54
2.11. Convergency of the sequence of harmonic bundles 58
2.12. Higgs field and twisted map 60
Chapter 3. Preliminary for Mixed Twistor Structure 62
3.1.
P1-holomorphic
vector bundle over X x P
1
62
3.2. Equivariant
P1-holomorphic
bundle over X
xF1
65
3.3. Tate objects and 0(p, q) 69
3.4. Equivalence of some categories 74
3.5. Variation of P1-holomorphic bundles 78
3.6. The twistor nilpotent orbit 84
3.7. Split polarized mixed twistor structure and the nilpotent orbit 89
3.8. The induced tuple on the divisor 96
3.9. Translation of some results due to Kashiwara, Kawai and Saito 100
3.10. 7^-triple in dimension 0 and twistor structure 107
Chapter 4. Preliminary for Filtrations 114
4.1. Filtrations and decompositions on a vector space 114
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