On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles
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.
irregular singularities, resolution of turning points
scientific article; zbMATH DE number 5689408
scientific article