Albanese map for Kähler manifolds with nef anticanonical bundle
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913238261694464 |
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| author | Naumann, Philipp Wu, Xiaojun |
| author_facet | Naumann, Philipp Wu, Xiaojun |
| contents | We study the structure of the Albanese map for Kähler manifolds with nef anticanonical bundle. First, we give a result for fourfolds whose Albanse torus is an elliptic curve. In the general case of any dimension, we look at two cases: The general fiber of the Albanese map is a Calabi-Yau manifold or a projective space. In the first case, we show that the manifold itself must be Calabi-Yau. In the second case, we give a more topological proof of a result by Cao and Höring which says that the manifold must be a projectivization of a numerically flat vector bundle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_06695 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Albanese map for Kähler manifolds with nef anticanonical bundle Naumann, Philipp Wu, Xiaojun Algebraic Geometry Complex Variables Differential Geometry 32J25 (Primary) 53C25, 14E30 (Secondary) We study the structure of the Albanese map for Kähler manifolds with nef anticanonical bundle. First, we give a result for fourfolds whose Albanse torus is an elliptic curve. In the general case of any dimension, we look at two cases: The general fiber of the Albanese map is a Calabi-Yau manifold or a projective space. In the first case, we show that the manifold itself must be Calabi-Yau. In the second case, we give a more topological proof of a result by Cao and Höring which says that the manifold must be a projectivization of a numerically flat vector bundle. |
| title | Albanese map for Kähler manifolds with nef anticanonical bundle |
| topic | Algebraic Geometry Complex Variables Differential Geometry 32J25 (Primary) 53C25, 14E30 (Secondary) |
| url | https://arxiv.org/abs/2310.06695 |