On Finite Parts of Divergent Complex Geometric Integrals and Their Dependence on a Choice of Hermitian Metric

2023/01/18 by Ludvig Svensson, Svensson, Ludvig · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2301.07417

openalex publication_date 2023/01/18 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28

Abstract

Let X be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on X that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle E → X. Given a choice of Hermitian metric on E we define a finite part of the divergent integral. Our main result is an explicit formula for the dependence on the choice of metric of the finite part.

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