Random zero currents of sections of Hermitian line bundles over compact Riemannian manifolds

2023/12/03 by Felix Knöppel, Knöppel, Felix
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2312.01493

openalex publication_date 2023/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with zero currents of random section of a Hermitian line bundle E over a compact oriented Riemannian manifold. Given a metric connection, heat flow yields a natural 1-parameter family of probability measures on the space of smooth sections ΓE. It is shown that the corresponding family of random zero currents connects the curvature of the bundle to the ground state zero current.

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