Abstract
We review work by Campana–Oguiso–Peternell (J Differ Geom 85(3):397–424, 2010) and Verbitsky (Geom Funct Anal 19(5):1481–1493, 2010) showing that a semi-positive line bundle on a hyperkähler manifold admits at least one non-trivial section. This is modest but tangible evidence towards the SYZ conjecture for hyperkähler manifolds.
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This review was prepared in the context of the seminar organized by the ERC Synergy Grant HyperK, Grant agreement ID 854361. The talk was delivered on April 16, 2021.
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Anella, F., Huybrechts, D. Effectivity of Semi-positive Line Bundles. Milan J. Math. 90, 389–401 (2022). https://doi.org/10.1007/s00032-022-00356-z
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DOI: https://doi.org/10.1007/s00032-022-00356-z