Hyperkahler SYZ conjecture and semipositive line bundles
Abstract
Let $M$ be a compact, holomorphic symplectic Kaehler manifold, and $L$ a non-trivial line bundle admitting a metric of semi-positive curvature. We show that some power of $L$ is effective. This result is related to the hyperkaehler SYZ conjecture, which states that such a manifold admits a holomorphic Lagrangian fibration, if $L$ is not big.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2008
- DOI:
- 10.48550/arXiv.0811.0639
- arXiv:
- arXiv:0811.0639
- Bibcode:
- 2008arXiv0811.0639V
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- 21 pages, v. 2.0, many references added, many minor corrections