On the V-filtration of D-modules

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In this mostly expository note we give a down-to-earth introduction to the V-filtration of M. Kashiwara and B. Malgrange on D-modules. We survey some applications to generalized Bernstein-Sato polynomials, multiplier ideals, and monodromy of vanishing cycles.
To appear in "Geometric methods in algebra and number theory" Proceedings of a December 2003 conference at the University of Miami, edited by F. Bogomolov and Yu. Tschinkel

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