2024/02/12 by Qianyu Chen, Chen, Qianyu, Bradley Dirks +3
Engineering · #14B05 #14F10 #32S40 #Aerosol Filtration and Electrostatic Precipitation #Algebraic Geometry (math.AG) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows
paper · pdf · doi:10.48550/arxiv.2402.07816
openalex publication_date 2024/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.