Kobayashi Hitchin Correspondence for Tame Harmonic Bundles and an Application 1st Edition by Takuro Mochizuki ISBN B09T5KT1L8 9783030944995

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Product details:
ISBN 10: B09T5KT1L8
ISBN 13: 9783030944995
Author: Takuro Mochizuki
We establish the correspondence between tame harmonic bundles and μL-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for μL-stable parabolic Higgs bundles. Then we show that any local system on a smooth quasi projective variety can be deformed to a variation of polarized Hodge structure. As a consequence, we can conclude that some kind of discrete groups cannot be a split quotient of the fundamental group of a smooth quasi projective variety.

Kobayashi Hitchin Correspondence for Tame Harmonic Bundles and an Application 1st Edition Table of contents:

• Introduction
  1.1 Main Results
  1.2 Methods and Difficulty
  1.3 Acknowledgement

• Preliminary
  2.1 Generality of Regular Filtered λ-Flat Sheaf in Complex Geometry
  2.2 Generality for λ-connection in the C∞-category
  2.3 Parabolic λ-flat Bundles Associated to Tame Harmonic Bundles
  2.4 Review of Existence Result of a Hermitian-Einstein Metric due to Simpson
  2.5 Review of Donaldson Functional
  2.6 The Integral of the Pseudo Curvature of Non-flat λ-connection on a Curve

• Ordinary Metric and Some Consequences
  3.1 Around the Intersection of the Divisor
  3.2 Around the Smooth Part of the Divisor
  3.3 Global Construction of a Metric
  3.4 Preliminary Existence Result of a Hermitian-Einstein Metric
  3.5 Some Formulas and Vanishings of Characteristic Numbers

• Continuity of Some Families of Harmonic Metrics
  4.1 Statements
  4.2 Preliminary from Elementary Calculus
  4.3 A Family of the Metrics for Logarithmic Flat λ-bundle of Rank Two on a Disc
  4.4 A Family of Metrics of a Parabolic Flat Bundle on a Disc
  4.5 Proof of Proposition 4.1

• The Existence of a Pluri-Harmonic Metric
  5.1 Preliminary
  5.2 The Surface Case
  5.3 Correspondences

• Filtered Local System
  6.1 Definition
  6.2 Correspondence

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Takuro Mochizuki,Kobayashi Hitchin,Correspondence,Tame Harmonic,Bundles,Application