Mathematical Research Letters

Volume 20 (2013)

Number 5

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

Pages: 951 – 959

DOI: http://dx.doi.org/10.4310/MRL.2013.v20.n5.a11

Authors

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

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

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

14E30, 14J40, 32Q15, 53C26

Full Text (PDF format)