1994/03/01 by Xian Wu, Wu, Xian
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algorithm #Decomposition #FOS: Mathematics #Geography #Geometric and Algebraic Topology #Intersection (aeronautics) #Linear subspace #Mathematics #Pure mathematics #Residual #Simple (philosophy) #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9403001
23 pages, Ams-Tex Version 2.1
arxiv created 1994/03/01 · openalex publication_date 1994/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We give a new residual intersection decomposition for the refined intersection products of Fulton-MacPherson. Our formula refines the celebrated residual intersection formula of Fulton, Kleiman, Laksov, and MacPherson. The new decomposition is more likely to be compatible with the canonical decomposition of the intersection products and each term in the decomposition thus has simple geometric meaning. Our study is motivated by its applications to some geometric problems. In particular, we use the decomposition to find the distribution of limiting linear subspaces in degenerations of hypersurfaces. A family of identities for characteristic classes of vector bundles is also obtained as another consequence. This paper will appear in Duke Math. Jour.