On the dual positive cones and the algebraicity of a compact Kähler manifold
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866913162739056640 |
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| author | Lin, Hsueh-Yung |
| author_facet | Lin, Hsueh-Yung |
| contents | We investigate the algebraicity of compact Kähler manifolds admitting a positive rational Hodge class of bidimension $(1,1)$. We prove that if the dual Kähler cone of a compact Kähler manifold $X$ contains a rational class as an interior point, then its Albanese variety is projective. As a consequence, we answer the Oguiso--Peternell problem for Ricci-flat compact Kähler manifolds. We also study related algebraicity problems for threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_10654 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the dual positive cones and the algebraicity of a compact Kähler manifold Lin, Hsueh-Yung Algebraic Geometry Complex Variables We investigate the algebraicity of compact Kähler manifolds admitting a positive rational Hodge class of bidimension $(1,1)$. We prove that if the dual Kähler cone of a compact Kähler manifold $X$ contains a rational class as an interior point, then its Albanese variety is projective. As a consequence, we answer the Oguiso--Peternell problem for Ricci-flat compact Kähler manifolds. We also study related algebraicity problems for threefolds. |
| title | On the dual positive cones and the algebraicity of a compact Kähler manifold |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2001.10654 |