2012/08/25 by R. Callejas-Bedregal, M. F. Z. Morgado, Callejas-Bedregal, R. +4
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AG #math.CV
paper · pdf · doi:10.48550/arxiv.1208.5084
arxiv created 2012/08/25 · openalex publication_date 2012/08/25 · arxiv updated 2012/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we study algebraic, geometric and topological properties of the Milnor classes of local complete intersections with arbitrary singularities. We describe first the Milnor class of the intersection of a finite number of hypersurfaces, under certain conditions of transversality, in terms of the Milnor classes of the hypersurfaces. Using this description we obtain a Parusiński-Pragacz type formula, an Aluffi type formula and a description of the Milnor class of the local complete intersection in terms of the global Lê cycles of the hypersurfaces that define it. We consider next the general case of a local complete intersection Z(s) defined by a regular section s of a rank r holomorphic bundle E over a compact manifold M, r ≥ 2. We notice that s determines a hypersurface Z( s) in the total space of the projectivization ℙ(E\vee) of the dual bundle E\vee, and we give a formula expressing the total Milnor class of the local complete intersection Z(s) in terms of the Milnor classes of the hypersurface Z( s).