Residual intersection theory with reducible schemes

2001/11/07 by Georg Hein, Hein, Georg
Mathematics · #14C17 #14N10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14C17 #msc:14N10

paper · pdf · doi:10.48550/arxiv.math/0111075

9 pages

arxiv created 2001/11/07 · openalex publication_date 2001/11/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a formula (Theorem 5.1) which allows to compute top Chern classes of vector bundles on the vanishing locus V(s) of a section of this bundle. This formula particularly applies in the case when V(s) is the union of locally complete intersections giving the individual contribution of each component and their mutual intersections. We conclude with applications to the enumeration of rational curves in complete intersections in projective space.

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