, Volume 19, Issue 5, pp 1481-1493
Date: 19 Dec 2009

Hyperkähler Syz Conjecture and Semipositive Line Bundles

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Abstract

Let M be a compact, holomorphic symplectic Kähler manifold, and L a non-trivial line bundle admitting a metric of semipositive curvature. We show that some power of L is effective. This result is related to the hyperkähler SYZ conjecture, which states that such a manifold admits a holomorphic Lagrangian fibration, if L is not big.