Kobayashi-Hitchin correspondence for tame harmonic bundles and an application
By: Takuro Mochizuki.
Series: Astérisque -- 309.
Publisher: Société mathématique de France
Published: 2006
Place of publication: Paris
Language: eng
Number of pages: 117
ISBN-13: 9782856292266
Subjects: Kobayashi-Hitchin correspondence (Algebraic geometry); Vector bundles.
Description: The author establishes the correspondence between tame harmonic bundles and $\mu --L$-polystable parabolic Higgs bundles with trivial characteristic numbers. He also shows the Bogomolov-Gieseker type inequality for $\mu --L$-stable parabolic Higgs bundles. The author shows that any local system on a smooth quasiprojective variety can be deformed to a variation of polarized Hodge structure. He then concludes that some kind of discrete groups cannot be a split quotient of the fundamental group of a smooth quasiprojective variety.
Notes: Includes bibliographical references (p. [113]-117).

Abstract also in French.