2015/10/07 by Joerg Schuermann, Schuermann, Joerg · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1510.01986
openalex publication_date 2015/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we compare different notions of transversality for possible singular complex algebraic or analytic subsets of an ambient complex manifold and prove a refined intersection formula for their Chern-Schwartz-MacPherson classes. In case of a transversal intersection of complex Whitney stratified sets, this result is well known. For splayed subsets it was conjectured (and proven in some cases) by Aluffi and Faber. Both notions are stronger than a micro-local "non-characteristic intersection" condition for the characteristic cycles of (associated) constructible functions, which nevertheless is enough to imply the asked refined intersection formula for the Chern-Schwartz-MacPherson classes. The proof is based the multiplicativity of Chern-Schwartz-MacPherson classes with respect to cross products, as well as a new Verdier-Riemann-Roch theorem for "non-characteristic pullbacks".