Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.08669 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912650798039040 |
|---|---|
| author | Wang, Zhenqu Zhang, Zhenlei |
| author_facet | Wang, Zhenqu Zhang, Zhenlei |
| contents | We introduce and construct a novel type of canonical metric: the semi-flat constant scalar curvature Kähler (semi-flat cscK) current, which naturally arises in Calabi-Yau fibrations. For a given elliptic surface $X$ with a holomorphic section, We explicitly construct the desired semi-flat cscK current and analyze its behavior along singular parts. We establish its uniqueness under the condition that $X$ possesses at least one singular fiber other than of type $I_b$ or $I_b^*$. These results contribute to a geometric uniformization program for elliptic surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08669 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-flat constant scalar curvature Kähler metric on elliptic surface Wang, Zhenqu Zhang, Zhenlei Differential Geometry We introduce and construct a novel type of canonical metric: the semi-flat constant scalar curvature Kähler (semi-flat cscK) current, which naturally arises in Calabi-Yau fibrations. For a given elliptic surface $X$ with a holomorphic section, We explicitly construct the desired semi-flat cscK current and analyze its behavior along singular parts. We establish its uniqueness under the condition that $X$ possesses at least one singular fiber other than of type $I_b$ or $I_b^*$. These results contribute to a geometric uniformization program for elliptic surfaces. |
| title | Semi-flat constant scalar curvature Kähler metric on elliptic surface |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2509.08669 |