An Introduction to V -Filtrations

Qianyu Chen (), Bradley Dirks () and Mircea Mustaţă ()
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Qianyu Chen: University of Michigan
Bradley Dirks: Stony Brook University
Mircea Mustaţă: University of Michigan

Chapter Chapter 11 in Handbook of Geometry and Topology of Singularities VII, 2025, pp 553-642 from Springer

Abstract: Abstract We give an introduction to the theory of V -filtrations of Malgrange and Kashiwara. After discussing the basic properties of this construction (in the case of a smooth hypersurface and, later, in the general case), we describe the connection with the theory of b-functions. As an example, we treat the case of weighted homogeneous isolated singularities. We discuss the compatibility of V -filtrations with proper push-forward and duality and the connection with nearby and vanishing cycles via the Riemann-Hilbert correspondence. We end by describing some invariants of singularities via the V -filtration.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-68711-2_11

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DOI: 10.1007/978-3-031-68711-2_11

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