Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zariski F-decomposition and Lagrangian fibration on hyperk\"ahler
  manifolds   For a compact hyperk\"ahler manifold X, we show certain Zariski decomposition
for every pseudo-effective R-divisor, and give a sufficient condition for X to
be bimeromorphic to a (holomorphic) Lagrangian fibration. We also prove that
any sequence of D-flops between projective hyperk\"ahler manifolds terminates
after finite steps.

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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg