Electronic ISBN:  9781470404741 
Product Code:  MEMO/185/870.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 185; 2007; 240 ppMSC: Primary 14; 32; 53;
The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies.
As another application, the author establishes the correspondence of semisimple regular holonomic \(D\)modules and polarizable pure imaginary pure twistor \(D\)modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author. 
Table of Contents

Chapters

Part 4. An application to the theory of pure twistor $D$modules

Chapter 14. Pure twistor $D$module

Chapter 15. Prolongation of $\mathcal {R}$module $\mathcal {E}$

Chapter 16. The filtrations of $\mathfrak {C}[\eth _t]$

Chapter 17. The weight filtration on $\psi _{t,u} \mathfrak {C}$ and the induced $\mathcal {R}$triple

Chapter 18. The sesquilinear pairings

Chapter 19. Polarized pure twistor $D$module and tame harmonic bundles

Chapter 20. The pure twistor $D$modules on a smooth curve (Appendix)

Part 5. Characterization of semisimplicity by tame pure imaginary pluriharmonic metric

Chapter 21. Preliminary

Chapter 22. Tame pure imaginary harmonic bundle

Chapter 23. The Dirichlet problem in the punctured disc case

Chapter 24. Control of the energy of twisted maps on a Kahler surface

Chapter 25. The existence of tame pure imaginary pluriharmonic metric


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The author studies the asymptotic behaviour of tame harmonic bundles. First he proves a local freeness of the prolongment of deformed holomorphic bundle by an increasing order. Then he obtains the polarized mixed twistor structure from the data on the divisors. As one of the applications, he obtains the norm estimate of holomorphic or flat sections by weight filtrations of the monodromies.
As another application, the author establishes the correspondence of semisimple regular holonomic \(D\)modules and polarizable pure imaginary pure twistor \(D\)modules through tame pure imaginary harmonic bundles, which is a conjecture of C. Sabbah. Then the regular holonomic version of M. Kashiwara's conjecture follows from the results of Sabbah and the author.

Chapters

Part 4. An application to the theory of pure twistor $D$modules

Chapter 14. Pure twistor $D$module

Chapter 15. Prolongation of $\mathcal {R}$module $\mathcal {E}$

Chapter 16. The filtrations of $\mathfrak {C}[\eth _t]$

Chapter 17. The weight filtration on $\psi _{t,u} \mathfrak {C}$ and the induced $\mathcal {R}$triple

Chapter 18. The sesquilinear pairings

Chapter 19. Polarized pure twistor $D$module and tame harmonic bundles

Chapter 20. The pure twistor $D$modules on a smooth curve (Appendix)

Part 5. Characterization of semisimplicity by tame pure imaginary pluriharmonic metric

Chapter 21. Preliminary

Chapter 22. Tame pure imaginary harmonic bundle

Chapter 23. The Dirichlet problem in the punctured disc case

Chapter 24. Control of the energy of twisted maps on a Kahler surface

Chapter 25. The existence of tame pure imaginary pluriharmonic metric