Geometric and Functional Analysis

, Volume 19, Issue 5, pp 1481–1493

Hyperkähler Syz Conjecture and Semipositive Line Bundles


DOI: 10.1007/s00039-009-0037-z

Cite this article as:
Verbitsky, M. Geom. Funct. Anal. (2010) 19: 1481. doi:10.1007/s00039-009-0037-z


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.

Keywords and phrases

Hyperkähler manifoldnef bundle

2000 Mathematics Subject Classification


Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Institute of Theoretical and Experimental PhysicsMoscowRussia