Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.17991 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- We consider divergent integrals $\int_X ω$ of certain forms $ω$ on a reduced pure-dimensional complex space $X$. The forms $ω$ are singular along a subvariety defined by the zero set of a holomorphic section $s$ of some holomorphic vector bundle $E$. Equipping $E$ with a smooth Hermitian metric allows us to define a finite part $\mathrm{fp}\,\int_X ω$ of the divergent integral as the action of a certain current extension of $ω$. We introduce a current calculus to compute finite parts for a special class of $ω$. Our main result is a formula that decomposes the finite part of such an $ω$ into sums of products of explicit currents. Lastly, we show that, in principle, it is possible to reduce the computation of $\mathrm{fp}\,\int_X ω$ for a general $ω$ to this class.