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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