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Mathematics > Complex Variables
Title: On Finite Parts of Divergent Complex Geometric Integrals and Their Dependence on a Choice of Hermitian Metric
(Submitted on 18 Jan 2023 (v1), last revised 25 Apr 2024 (this version, v3))
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 $E \rightarrow X$. 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.
Submission history
From: Ludvig Svensson [view email][v1] Wed, 18 Jan 2023 10:26:26 GMT (25kb)
[v2] Mon, 18 Sep 2023 14:24:41 GMT (27kb)
[v3] Thu, 25 Apr 2024 13:41:00 GMT (28kb)
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