The zeros of random sections of real vector bundles

2024/04/11 by Boris Kazarnovskii, Kazarnovskii, Boris
Mathematics · #52Axx #60D05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #G.3 #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2404.07596

openalex publication_date 2024/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define integral geometric analogues of the Chern classes for real vector bundle on a smooth real variety. More precisely, we define the Chern densities of a real bundle. These densities are analogues of the Chern forms of a complex vector bundle and inherit some of their properties. \noindent (The text is a summary of a report on the conference PCA'2024 in Euler International Mathematical Institute, St. Petersburg)

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