Geodesic
On the dual positive cones and the algebraicity of a compact Kähler manifold
Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023)

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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.
DOI : 10.46298/epiga.2024.10771
Classification : 32J27 
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     author = {Lin, Hsueh-Yung},
     title = {On the dual positive cones and the algebraicity of a compact {K\"ahler} manifold},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     year = {2023},
     doi = {10.46298/epiga.2024.10771},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2024.10771/}
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Lin, Hsueh-Yung. On the dual positive cones and the algebraicity of a compact Kähler manifold. Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023). doi: 10.46298/epiga.2024.10771

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