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An Introduction to V -Filtrations

In: Handbook of Geometry and Topology of Singularities VII

Author

Listed:
  • Qianyu Chen

    (University of Michigan)

  • Bradley Dirks

    (Stony Brook University)

  • Mircea Mustaţă

    (University of Michigan)

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.

Suggested Citation

  • Qianyu Chen & Bradley Dirks & Mircea Mustaţă, 2025. "An Introduction to V -Filtrations," Springer Books, in: José Luis Cisneros-Molina & Lê Dũng Tráng & José Seade (ed.), Handbook of Geometry and Topology of Singularities VII, chapter 0, pages 553-642, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-68711-2_11
    DOI: 10.1007/978-3-031-68711-2_11
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