A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910465938948096 |
|---|---|
| author | Graf, Patrick |
| author_facet | Graf, Patrick |
| contents | Let $X$ be a compact Kähler fourfold with klt singularities and vanishing first Chern class, smooth in codimension two. We show that $X$ admits a Beauville-Bogomolov decomposition: a finite quasi-étale cover of $X$ splits as a product of a complex torus and singular Calabi-Yau and irreducible holomorphic symplectic varieties. We also prove that $X$ has small projective deformations and the fundamental group of $X$ is projective. To obtain these results, we propose and study a new version of the Lipman-Zariski conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_06764 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four Graf, Patrick Algebraic Geometry Complex Variables Differential Geometry Let $X$ be a compact Kähler fourfold with klt singularities and vanishing first Chern class, smooth in codimension two. We show that $X$ admits a Beauville-Bogomolov decomposition: a finite quasi-étale cover of $X$ splits as a product of a complex torus and singular Calabi-Yau and irreducible holomorphic symplectic varieties. We also prove that $X$ has small projective deformations and the fundamental group of $X$ is projective. To obtain these results, we propose and study a new version of the Lipman-Zariski conjecture. |
| title | A decomposition theorem for singular Kähler spaces with trivial first Chern class of dimension at most four |
| topic | Algebraic Geometry Complex Variables Differential Geometry |
| url | https://arxiv.org/abs/2101.06764 |