Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1

Download or read book Asymptotic Behaviour of Tame Harmonic Bundles and an Application to Pure Twistor $D$-Modules, Part 1 written by Takuro Mochizuki and published by American Mathematical Soc.. This book was released on 2007 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.