On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles
type: Item
instance of: scholarly article
title: On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles
zbMATH Open document ID: 1202.32008
author: Takuro Mochizuki
publication date: 2010-04-06T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10473
review text: The paper under review is a brief survey of basic ideas and results in the study of resolution of turning points for meromorphic flat bundles and closely related with the theory of wild harmonic bundles developed by the author over the past few years. In fact, key ingredients of his study are the theory of Deligne-Malgrange lattices associated with meromorphic flat bundles on a complex manifold with poles along a normal crossing divisor and the method of Kobayashi-Hitchin correspondance for tame harmonic bundles. It should be noted that the Deligne-Malgrange lattice is nothing but the canonical lattice introduced by \textit{B. Malgrange} [Invent. Math. 124, No.~1--3, 367--387 (1996; Zbl 0849.32003)] in a more general context. Among other things the author explains how one can prove an extension of his main theorem [\textit{T. Mochizuki}, Advanced Studies in Pure Mathematics 54, 223--253 (2009; Zbl 1183.14027)] to the higher dimensional case.
reviewed by: Aleksandr G. Aleksandrov
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 53C07
zbMATH DE Number: 5689408
zbMATH Keywords: harmonic bundles
zbMATH Keywords: pluri-harmonic metrics
zbMATH Keywords: meromorphic flat bundles
zbMATH Keywords: semi-simplicity
zbMATH Keywords: Deligne-Malgrange lattices
zbMATH Keywords: irregular singularities, resolution of turning points
zbMATH Keywords: Kobayashi-Hitchin correspondence
MaRDI profile type: Publication
OpenAlex ID: W2521054625
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DOI: 10.5802/AIF.2509
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5689408