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.1208.5085
Version to be published in Inventiones Mathematicae, including an Errata
openalex publication_date 2012/08/25 · arxiv created 2013/07/18 · arxiv updated 2013/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this work is to establish a link between the theory of Chern classes for singular varieties and the geometry of the varieties in question. Namely, we show that if Z is a hypersurface in a compact complex manifold, defined by the zero-scheme of a nonzero holomorphic section of a very ample line bundle, then its Milnor classes, regarded as elements in the Chow group of Z, determine the global Lê cycles of Z; and viceversa: The Lê cycles determine the Milnor classes. Morally this implies, among other things, that the Milnor classes determine the topology of the local Milnor fibres at each point of Z, and the geometry of the local Milnor fibres determines the corresponding Milnor classes.