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arXiv · 2402.07816

An introduction to $V$-filtrations

Qianyu Chen·Bradley Dirks·Mircea Mustaţă
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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.

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Qianyu Chen, Bradley Dirks, Mircea Mustaţă. 2024-02-12. An introduction to $V$-filtrations. https://arxiv.org/abs/2402.07816

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