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.
| ISBN: | 9780821839423 |
| Publication date: | 30th December 2006 |
| Author: | Takuro Mochizuki |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 565 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Complex analysis, complex variables Differential and Riemannian geometry Algebraic geometry |