Hyperkahler SYZ conjecture and semipositive line bundles

Details Hyperkahler SYZ conjecture and semipositive line bundles Hyperkahler SYZ conjecture and semipositive line bundles

2008-11-05

arxiv.org/abs/0811.0639v2

GAFA 19, No. 5, 1481-1493 (2010)

Mathematics

Algebraic Geometry

21 pages, v. 2.0, many references added, many minor corrections

Scientific paper

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.

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