Compact Kähler three-folds with nef anti-canonical bundle
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910776173789184 |
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| author | Matsumura, Shin-ichi Wu, Xiaojun |
| author_facet | Matsumura, Shin-ichi Wu, Xiaojun |
| contents | In this paper, we prove that a non-projective compact Kähler three-fold with nef anti-canonical bundle is, up to a finite étale cover, one of the following: a manifold with vanishing first Chern class; the product of a K3 surface and the projective line; or a projective space bundle over a $2$-dimensional torus. This result extends Cao-Höring's structure theorem for projective manifolds to compact Kähler manifolds in dimension $3$. For the proof, we investigate the Minimal Model Program for compact Kähler three-folds with nef anti-canonical bundles by using the positivity of direct image sheaves, $\mathbb{Q}$-conic bundles, and orbifold vector bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_03163 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compact Kähler three-folds with nef anti-canonical bundle Matsumura, Shin-ichi Wu, Xiaojun Algebraic Geometry Complex Variables Differential Geometry Primary 32J25, Secondary 53C25, 14E30 In this paper, we prove that a non-projective compact Kähler three-fold with nef anti-canonical bundle is, up to a finite étale cover, one of the following: a manifold with vanishing first Chern class; the product of a K3 surface and the projective line; or a projective space bundle over a $2$-dimensional torus. This result extends Cao-Höring's structure theorem for projective manifolds to compact Kähler manifolds in dimension $3$. For the proof, we investigate the Minimal Model Program for compact Kähler three-folds with nef anti-canonical bundles by using the positivity of direct image sheaves, $\mathbb{Q}$-conic bundles, and orbifold vector bundles. |
| title | Compact Kähler three-folds with nef anti-canonical bundle |
| topic | Algebraic Geometry Complex Variables Differential Geometry Primary 32J25, Secondary 53C25, 14E30 |
| url | https://arxiv.org/abs/2304.03163 |