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arXiv · 2001.10654

On the dual positive cones and the algebraicity of a compact K\"ahler manifold

Hsueh-Yung Lin
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Abstract

We investigate the algebraicity of compact K\"ahler manifolds admitting a positive rational Hodge class of bidimension $(1,1)$. We prove that if the dual K\"ahler cone of a compact K\"ahler 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 K\"ahler manifolds. We also study related algebraicity problems for threefolds.

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Hsueh-Yung Lin. 2020-01-29. On the dual positive cones and the algebraicity of a compact K\"ahler manifold. https://doi.org/10.46298/epiga.2024.10771

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