Hypersurface Singularities and the Swing

2004/11/19 by Lê Dũng Tráng, Tráng, Lê Dũng, David B. Massey +1
Mathematics · #32B10 #32B15 #32C18 #32C35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:32B10 #msc:32B15 #msc:32C18 #msc:32C35

paper · pdf · doi:10.48550/arxiv.math/0411432

11 pages

openalex publication_date 2004/11/19 · arxiv created 2005/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that f defines a singular, complex affine hypersurface. If the critical locus of f is one-dimensional, we obtain new general bounds on the ranks of the homology groups of the Milnor fiber of f. This result has an interesting implication on the structure of the vanishing cycles in the category of perverse sheaves.

Related

• Hypersurface Singularities and Milnor Equisingularity
• A remark on vanishing cycles with two strata
• A Formula For the Homology Groups of the Milnor Fibres of an Isolated Real Hypersurface Singularity
• On Isolated Real Singularities I
• Topology of hypersurface singularities with 3-dimensional critical set