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Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2
 
Takuro Mochizuki Kyoto University, Kyoto, Japan
Front Cover for Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2
Available Formats:
Electronic ISBN: 978-1-4704-0474-1
Product Code: MEMO/185/870.E
240 pp 
List Price: $84.00
MAA Member Price: $75.60
AMS Member Price: $50.40
Front Cover for Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2
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  • Front Cover for Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2
  • Back Cover for Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2
Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 2
Takuro Mochizuki Kyoto University, Kyoto, Japan
Available Formats:
Electronic ISBN:  978-1-4704-0474-1
Product Code:  MEMO/185/870.E
240 pp 
List Price: $84.00
MAA Member Price: $75.60
AMS Member Price: $50.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1852007
    MSC: 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 sesqui-linear 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 pluri-harmonic 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 pluri-harmonic metric
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Volume: 1852007
MSC: 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.

  • 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 sesqui-linear 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 pluri-harmonic 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 pluri-harmonic metric
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