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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.06964 |
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| _version_ | 1866909972859715584 |
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| author | Ahn, Taeyong |
| author_facet | Ahn, Taeyong |
| contents | We investigate the intersection of positive closed currents in a general setting, employing tangent currents alongside King's residue formula. Our main result establishes a natural condition for the intersection--namely, the Dinh-Sibony product--of positive closed currents on domains and derives an integral representation of this intersection. In parallel, we study the existence, $h$-dimension, and shadow of tangent currents, extending our approach to the study of the self-intersection of analytic subsets. We also present a local version of superpotentials and a regularization of positive closed currents, explore the connections with slicing theory, and examine classical examples. Our work extends to general complex manifolds, including compact Kähler manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06964 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersection of Positive Closed Currents Ahn, Taeyong Complex Variables Differential Geometry We investigate the intersection of positive closed currents in a general setting, employing tangent currents alongside King's residue formula. Our main result establishes a natural condition for the intersection--namely, the Dinh-Sibony product--of positive closed currents on domains and derives an integral representation of this intersection. In parallel, we study the existence, $h$-dimension, and shadow of tangent currents, extending our approach to the study of the self-intersection of analytic subsets. We also present a local version of superpotentials and a regularization of positive closed currents, explore the connections with slicing theory, and examine classical examples. Our work extends to general complex manifolds, including compact Kähler manifolds. |
| title | Intersection of Positive Closed Currents |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2503.06964 |