Аннотация:
The SYZ conjecture claims that any non-ample nef bundle on a holomorphic symplectic manifold is semiample, and corresponds to a Lagrangian fibration. When a nef bundle $L$ admits a metric with semipositive curvature, cohomology of $L$ are in correspondence with holomorphic $L$-valued forms on $M$. Using stability and divisorial Zariski decomposition due to $S$. Boucksom, we show that some power of $L$ is effective. This method could be modified using multiplier ideals and Nadel vanishing to show that any nef bundle on a holomorphic symplectic manifold has a tensor power which is effective.
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