Bogomolov Decomposition and Compact K{ä}hler Manifolds of Algebraic Dimension Zero
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911698382749696 |
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| author | Campana, Frederic Bruno |
| author_facet | Campana, Frederic Bruno |
| contents | We prove conditionally that compact K\''ahler manifolds of algebraic dimension zero are (essentially) isogeneous to products of Kummer and `simple' ones, the latter being conjecturally bimeromorphically symplectic. `Simple' means: its general point is not contained in a nontrivial subvariety. We also prove that four-dimensional `strictly simple' manifolds are either étale quotients of tori or holomorphically symplectic. `Strictly simple' means: its only subvarieties are points and itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19713 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bogomolov Decomposition and Compact K{ä}hler Manifolds of Algebraic Dimension Zero Campana, Frederic Bruno Algebraic Geometry We prove conditionally that compact K\''ahler manifolds of algebraic dimension zero are (essentially) isogeneous to products of Kummer and `simple' ones, the latter being conjecturally bimeromorphically symplectic. `Simple' means: its general point is not contained in a nontrivial subvariety. We also prove that four-dimensional `strictly simple' manifolds are either étale quotients of tori or holomorphically symplectic. `Strictly simple' means: its only subvarieties are points and itself. |
| title | Bogomolov Decomposition and Compact K{ä}hler Manifolds of Algebraic Dimension Zero |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.19713 |