Mathematical Research Letters

Volume 20 (2013)

Number 5

Zariski $F$-decomposition and Lagrangian fibration on hyperkähler manifolds

Pages: 951 – 959



Daisuke Matsushita (Division of Mathematics, Graduate School of Science, Hokkaido University, Sapporo, Japan)

De-Qi Zhang (Department of Mathematics, National University of Singapore)


For a compact hyperkähler manifold $X$, we show certain Zariski decomposition for every pseudo-effective $\mathbb{R}$-divisor. We also prove that any sequence of $D$-flops between projective hyperkähler manifolds terminates after finitely many steps.


hyperkähler manifold, Zariski decomposition, Lagrangian fibration, termination of flops

2010 Mathematics Subject Classification

14E30, 14J40, 32Q15, 53C26

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