Cohomology Isomorphism of Symmetric Power of Cotangent Bundle of Ball quotient and Its Toroidal Compactification
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914252593299456 |
|---|---|
| author | Lee, Seungjae Seo, Aeryeong |
| author_facet | Lee, Seungjae Seo, Aeryeong |
| contents | In this paper, we investigate the $L^2$-Dolbeault cohomology of the symmetric power of cotangent bundles of ball quotients with finite volume, as well as their toroidal compactification. Through the application of Hodge theory for complete hermitian manifolds, we establish the existence of Hodge decomposition and Green's operator. Moreover, we extend the results by Adachi [A21] and Lee-Seo [LS23-2] from compact complex hyperbolic spaces to complex hyperbolic spaces with finite volume. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01931 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cohomology Isomorphism of Symmetric Power of Cotangent Bundle of Ball quotient and Its Toroidal Compactification Lee, Seungjae Seo, Aeryeong Complex Variables Differential Geometry In this paper, we investigate the $L^2$-Dolbeault cohomology of the symmetric power of cotangent bundles of ball quotients with finite volume, as well as their toroidal compactification. Through the application of Hodge theory for complete hermitian manifolds, we establish the existence of Hodge decomposition and Green's operator. Moreover, we extend the results by Adachi [A21] and Lee-Seo [LS23-2] from compact complex hyperbolic spaces to complex hyperbolic spaces with finite volume. |
| title | Cohomology Isomorphism of Symmetric Power of Cotangent Bundle of Ball quotient and Its Toroidal Compactification |
| topic | Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2311.01931 |