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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.

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  1. Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya, 25, Moscow, 117259, Russia

    Misha Verbitsky

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  1. Misha Verbitsky
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Verbitsky, M. Hyperkähler Syz Conjecture and Semipositive Line Bundles. Geom. Funct. Anal. 19, 1481–1493 (2010). https://doi.org/10.1007/s00039-009-0037-z

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