On the dual positive cones and the algebraicity of a compact Kähler manifold

Abstract

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.

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References in corpus (1)

• On the Log Abundance for Compact {K{ä}hler} threefolds II